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Pre-Calculus

This class was created by Brainscape user Anton Soloshenko. Visit their profile to learn more about the creator.

By: Anton Soloshenko
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Decks in this class (343)

The Top Ten List of Mistakes (1.1.1)
No notes
1  cards
Concepts of Inequality (1.2.1)
What does,
What does,
What does mean
11  cards
Inequalities and Interval Notation (1.2.2)
How do you restrict the range of ...
1  cards
Properties of Absolute Value (1.3.1)
How do you solve absolute value p...
1  cards
Evaluating Absolute Value Expressions (1.3.2)
Why is absolute value always posi...,
How do you solve large problems w...
2  cards
An Introduction to Exponents (1.4.1)
What are exponents
1  cards
Evaluating Exponential Expressions (1.4.2)
How do you solve problems with ex...
1  cards
Applying the Rules of Exponents (1.4.3)
Power,
Base,
Exponent
4  cards
Evaluating Expressions with Negative Exponents (1.4.4)
Dividing with exponents,
0 as an exponent,
Negative exponents
3  cards
Converting between Decimal and Scientific Notation (1.5.1)
Scientific notation,
Calculator presentation,
Numbers larger than 10
5  cards
Converting Rational Exponents and Radicals (1.5.2)
Radical,
Rational exponents,
Roots
3  cards
Simplifying Radical Expressions (1.6.1)
Negative exponent,
Rational exponents
2  cards
Simplifying Radical Expressions with Variables (1.6.2)
Radical expression,
Power of a power property,
Product of powers property
4  cards
Rationalizing Denominators (1.6.3)
Fractions,
Clearing a denominator,
Conjugate
4  cards
Determining Components and Degree (1.7.1)
Polynomial,
Coefficient,
The degree of a polynomial
4  cards
Adding, Subtracting, and Multiplying Polynomials (1.7.2)
Adding polynomials,
Like terms,
Subtracting polynomials
4  cards
Multiplying Big Products (1.7.3)
The distributive property,
Multiplying polynomials,
Like terms
3  cards
Using Special Products (1.7.4)
A b 2 a 2 2ab b 2,
A b 3 a 3 3a 2b 3ab 2 b 3,
Like terms
4  cards
Factoring Using the Greatest Common Factor (1.8.1)
Review,
Polynomial factoring
2  cards
Factoring by Grouping (1.8.2)
Grouping terms,
Deciding what to group is part of...
2  cards
Factoring Trinomials Completely (1.8.3)
Trinomial,
Factoring to do list,
Foil
4  cards
Factoring Trinomials: The Grouping Method (1.8.4)
A quadratic trinomial,
Standard form of a quadratic expr...,
Factoring a trionomial
3  cards
Factoring Perfect Square Trinomials (1.9.1)
Perfect square trinomial
1  cards
Factoring the Difference of Two Squares (1.9.2)
Remember that combining like term...,
Learn to notice where you can rew...,
What does the minus sign tell us ...
3  cards
Factoring the Sums and Differences of Cubes (1.9.3)
Sum of two cubes a 3 b 3 a b a 2 ...,
Difference of two cubes a 3 b 3 a...
2  cards
Factoring by Any Method (1.9.4)
Never get discouraged if your fir...,
Methods of factoring greatest com...
2  cards
Rational Expressions and Domain (1.10.1)
A rational expression is a fracti...,
The domain is the set of all valu...,
The domain of a rational expressi...
4  cards
Working with Fractions (1.10.2)
The common denominator is usually...,
To achieve a common denominator m...,
Canceling in a fraction multiplic...
4  cards
Writing Rational Expressions in Lowest Terms (1.10.3)
A rational expression is a polyno...,
Factor out any quantity common ac...,
Remember that the denominator can...
3  cards
Multiplying and Dividing Rational Expressions (1.11.1)
Multiplying and dividing rational...,
Multiplying rationals means a b c...,
Dividing rationals means a b c d ...
5  cards
Adding and Subtracting Rational Expressions (1.11.2)
Always find the common denominato...,
The least common denominator is t...,
The least common multiple is the ...
5  cards
Rewriting Complex Fractions (1.11.3)
The first step in simplifying a c...,
Two ways to simplify a complex fr...
2  cards
Introducing and Writing Complex Numbers (1.12.1)
Numbers like sqrt 4 or sqrt 95 th...,
Imaginary numbers can be written ...,
A complex number has the form a b...
3  cards
Rewriting Powers of i (1.12.2)
I sqrt 1 the number i is an examp...,
I 2 1,
I 3 i i 2 i 1 i
5  cards
Adding and Subtracting Complex Numbers (1.12.3)
A complex number is a binomial co...,
When adding complex numbers add l...,
When subtracting complex numbers ...
3  cards
Multiplying Complex Numbers (1.12.4)
I sqrt 1 this is called an imagin...,
I 2 1 this follows from the defin...,
Foil multiply binomials by multip...
3  cards
Dividing Complex Numbers (1.12.5)
Clearing a denominator of radical...,
A conjugate is used when fraction...,
I sqrt i
4  cards
An Introduction to Solving Equations (2.1.1)
What is an equation,
What is a variable,
What is a constant
3  cards
Solving a Linear Equation (2.1.2)
What are linear equations,
How do you solve linear equations
2  cards
Solving a Linear Equation with Rationals (2.1.3)
Cross multiplying,
Remove variables from the denomin...,
Warning no denominator can ever e...
3  cards
Solving a Linear Equation That Has Restrictions (2.1.4)
When solving linear equations,
When working with equations the t...,
Some equations have no solution t...
3  cards
An Introduction to Solving Word Problems (2.2.1)
Working a word problem requires b...,
Word problem solving process 1 de...,
Working a word problem is first o...
4  cards
Solving for Perimeter (2.2.2)
Word problems require translation...,
Formula a generalized equation fo...,
Always check when you re done to ...
4  cards
Solving a Linear Geometry Problem (2.2.3)
A right circular cylinder is the ...,
The volume of a right cylinder ca...,
Define the variables h the height...
3  cards
Solving for Consecutive Numbers (2.2.4)
Consecutive numbers counting numb...,
Consecutive even numbers even num...,
Consecutive odd numbers odd numbe...
7  cards
Solving to Find the Average (2.2.5)
To find the average add all the t...,
To get a desired average you must...,
Add all numbers than divide by th...
3  cards
Solving for Constant Velocity (2.3.1)
A constant velocity problem invol...,
Use the formula d rt to write an ...
2  cards
Solving a Problem about Work (2.3.2)
A linear work problem calculates ...,
This type of problem asks that tw...,
Since the problem asks about time...
6  cards
Solving a Mixture Problem (2.3.3)
Mixture problems word problems th...,
Tricks for mixture problems make ...,
Remember the translation process ...
6  cards
Solving an Investment Problem (2.3.4)
Investment problem a word problem...,
Reading the question is always th...
2  cards
Solving Business Problems (2.3.5)
Solving problems involving prices...,
Remember as always reading the wo...,
Define the variable
5  cards
Solving Quadratics by Factoring (2.4.1)
Quadratic equations have a square...,
One method for solving a quadrati...,
The solution s of a quadratic equ...
4  cards
Solving Quadratics by Completing the Square (2.4.2)
Completing the square is a proces...,
You have two ways to solve this p...
2  cards
Completing the Square: Another Example (2.4.3)
When a square term has a coeffici...,
Next move the constant term to th...
2  cards
Proving the Quadratic Formula (2.5.1)
Completing the square for a gener...,
Begin with a generalized equation...,
X b sqrt b 2 4ac 2a
3  cards
Using the Quadratic Formula (2.5.2)
Using the quadratic formula allow...,
Quadratic equation ax 2 bx c 0,
X b sqrt b 2 4ac 2a
5  cards
Predicting the Type of Solutions Using the Discriminant (2.5.3)
The discriminant is the quantity ...,
The discriminant for the equation...,
The discriminant is important bec...
5  cards
Solving for a Squared Variable (2.6.1)
The example used in this lecture ...,
The quadratic formula gives us an...,
Here s an example using the quadr...
3  cards
Finding Real Number Restrictions (2.6.2)
The denominator can never have a ...,
The domain of the variable is the...,
To find any value of the variable...
7  cards
Solving Fancy Quadratics (2.6.3)
Frequently an equation that appea...,
Be creative with your use of vari...,
Remember that whenever you solve ...
5  cards
An Introduction to Word Problems with Quadratics (2.7.1)
How do you solve quadratic word p...
1  cards
Solving a Quadratic Geometry Problem (2.7.2)
Process for solving word problems...,
Geometry problems generally use a...,
In reading this problem you find ...
5  cards
Solving with the Pythagorean Theorem (2.7.3)
The pythagorean theorem states th...
1  cards
The Pythagorean Theorem: Another Example (2.7.4)
The pythagorean theorem states th...
1  cards
Solving a Motion Problem (2.8.1)
Process for solving word problems...,
This type of motion problem relat...,
The first thing to do always is t...
3  cards
Solving a Projectile Problem (2.8.2)
Use the quadratic formula to solv...
1  cards
Solving Other Problems (2.8.3)
When working with problems with d...,
In landing an aircraft the pilot ...
2  cards
Determining Extraneous Roots (2.9.1)
Extraneous roots are solutions th...,
Always check all solutions in the...,
Always check your answer when you...
5  cards
Solving an Equation Containing a Radical (2.9.2)
To solve an equation containing a...,
If one side of the equation is no...,
Extraneous roots do exist for the...
5  cards
Solving an Equation with Two Radicals (2.9.3)
Solving a radical equation genera...,
When an equation has two radicals...,
Once you have solved your non rad...
3  cards
Solving an Equation with Rational Exponents (2.9.4)
To solve an equation containing a...,
To solve an equation containing t...,
Extraneous solutions do exist for...
5  cards
An Introduction to Variation (2.10.1)
Variation is the notion that two ...,
If two quantities are directly pr...,
Two quantities usually are direct...
7  cards
Direct Proportion (2.10.2)
Hooke s law says that the distanc...,
If two quantities are directly pr...,
Two quantities usually are direct...
6  cards
Inverse Proportion (2.10.3)
If two quantities are inversely p...,
If some value x is inversely prop...,
If two inversely proportional val...
4  cards
An Introduction to Solving Inequalities (2.11.1)
Indicates that the quantity on th...,
•,
Indicates that the quantity on th...
7  cards
Solving Compound Inequalities (2.11.2)
A compound inequality consists of...,
And means that both inequalities ...,
Graphing both solutions on a numb...
6  cards
More on Compound Inequalities (2.11.3)
Remember to reverse the inequalit...,
In this or example our solution s...
2  cards
Solving Word Problems Involving Inequalities (2.11.4)
Word problem solving process dete...,
Read the problem and see what fac...
2  cards
Solving Quadratic Inequalities (2.12.1)
Solving inequalities factor where...,
Remember that multiplying or divi...,
Remember that graphing on a numbe...
4  cards
Solving Quadratic Inequalities: Another Example (2.12.2)
Solving inequalities factor where...,
Remember that multiplying or divi...,
Remember that graphing on a numbe...
4  cards
Solving Rational Inequalities (2.13.1)
A rational inequality is an inequ...,
The solution for a rational inequ...,
Steps for solving a rational ineq...
7  cards
Solving Rational Inequalities (2.13.2)
Solving inequalities factor where...,
Remember to carefully watch that ...,
The mission in this problem is to...
3  cards
Determining the Domains of Expressions with Radicals (2.13.3)
The domain is the set of all valu...,
The radicand is the value or expr...,
Solving inequalities factor where...
4  cards
Matching Number Lines with Absolute Values (2.14.1)
Absolute value is the distance a ...,
An absolute value with a less tha...,
An absolute value with a greater ...
5  cards
Solving Absolute Value Equations (2.14.2)
The absolute value of a number st...,
The notation for absolute value p...,
If the absolute value of a number...
6  cards
Solving Equations with Two Absolute Value Expressions (2.14.3)
Some equations have two absolute ...,
Set up your two possible equation...,
Check your answers in the origina...
6  cards
Solving Absolute Value Inequalities (2.14.4)
Absolute values within inequaliti...,
If the absolute value is less tha...,
If the absolute value is greater ...
6  cards
Solving Absolute Value Inequalities: More Examples (2.14.5)
The best way to work with absolut...,
Remember when an equation offers ...,
Any absolute value will be positi...
4  cards
Using the Cartesian System (3.1.1)
X axis the horizontal scale for m...,
Y axis the vertical scale for mea...,
Origin the point where the two sc...
7  cards
Thinking Visually (3.1.2)
An axis is the scale which measur...,
The origin is the point where the...,
A horizontal axis measures horizo...
10  cards
Finding the Distance between Two Points (3.2.1)
The distance formula is an applic...,
The midpoint formula determines t...,
Draw your given line segment firs...
3  cards
Finding the Second Endpoint of a Segment (3.2.2)
Any point s location is given by ...,
If you are given an endpoint and ...
2  cards
Collinearity and Distance (3.3.1)
Points that fall on the same line...,
Three points are collinear if for...,
Three points are not collinear if...
7  cards
Triangles (3.3.2)
Collinear any two or more points ...,
Three points are collinear any ti...,
Three points form a triangle any ...
5  cards
Finding the Center-Radius Form of the Equation of a Circle (3.4.1)
A circle is the set of all points...,
The center of a circle is usually...,
Any point x y mentioned in relati...
6  cards
Finding the Center and Radius of a Circle (3.4.2)
Completing the square reduce the ...,
Watch your signs when stating the...,
Frequently you are given an equat...
3  cards
Decoding the Circle Formula (3.4.3)
Equation of a circle x h 2 y k 2 r 2,
The center of a circle is represe...,
The radius is the distance from t...
4  cards
Solving Word Problems Involving Circles (3.4.4)
Find all points where x y ie the ...,
There are many circles that pass ...
2  cards
Graphing Equations by Locating Points (3.5.1)
One way to graph a line is to pic...,
Whenever you see one variable squ...,
Whenever you see a variable insid...
5  cards
Finding the x- and y- Intercepts of an Equation (3.5.2)
An x intercept is a point where a...,
A y intercept is a point where a ...,
A line will have one x intercept ...
5  cards
Functions and the Vertical Line Test (3.6.1)
A relation is a set of ordered pa...,
A function is a set of ordered pa...,
If each time you use a specific v...
3  cards
Identifying Functions (3.6.2)
A function is an equation where y...,
Vertical line test for a function...,
For an equation to be a function ...
3  cards
Function Notation and Finding Function Values (3.6.3)
Function notationreplaces the y i...,
F x shows the y value for the giv...,
F x is read f of x the expression...
4  cards
Determining Intervals Over Which a Function is Increasing (3.7.1)
A function is decreasing if the g...,
A function is increasing if the g...,
A function is constant if it is n...
9  cards
Evaluating Piecewise-Defined Functions for Given Values (3.7.2)
A piecewise defined function is d...,
To evaluate a piecewise defined f...,
To graph a piecewise defined func...
4  cards
Solving Word Problems Involving Functions (3.7.3)
Function thinking allows you to s...,
F x means a function defined in t...,
For any rectangle perimeter 2l 2w...
5  cards
Finding the Domain and Range of a Function (3.8.1)
The domain of a function is the s...,
The range of a function is the se...,
Values excluded from the domain i...
4  cards
Domain and Range: One Explicit Example (3.8.2)
The domain of a function is the s...,
Values of x must be excluded from...,
The range of a function is the se...
5  cards
Satisfying the Domain of a Function (3.8.3)
The domain is the set of all real...,
R is the notational symbol for th...,
R a1 a2 is the notation for a dom...
4  cards
An Introduction to Slope (3.9.1)
The graph of any linear function ...,
In algebra the degree of steepnes...,
Every line has some degree of ste...
3  cards
Finding the Slope of a Line Given Two Points (3.9.2)
Slope is the change from one poin...,
Slope is the measure of pitch or ...,
In the slope formula the x1 y1 x2...
4  cards
Interpreting Slope from a Graph (3.9.3)
A positive slope indicates that a...,
A negative slope indicates that a...,
The steeper a line rises or falls...
6  cards
Graphing a Line Using Point and Slope (3.9.4)
Slope rise run change in y change...,
A positive slope indicates that a...,
A negative slope indicates that a...
4  cards
Writing an Equation in Slope-Intercept Form (3.10.1)
Standard equation of a line ax by...,
Slope intercept equation of a lin...,
The y intercept is the point wher...
6  cards
Writing an Equation Given Two Points (3.10.2)
Standard equation of a line ax by...,
Slope intercept equation of a lin...,
The y intercept is the point wher...
6  cards
Writing an Equation in Point-Slope Form (3.10.3)
The point slope form of an equati...,
Again you are substituting values...
2  cards
Matching a Slope-Intercept Equation with Its Graph (3.10.4)
Slope intercept equation of a lin...,
The point slope form of an equati...,
Consider the example given here y...
4  cards
Slope for Parallel and Perpendicular Lines (3.10.5)
Two lines are parallel when they ...,
Two lines are perpendicular when ...,
When two lines are parallel they ...
8  cards
Constructing Linear Function Models of Data (3.11.1)
Slope can be very useful for the ...,
Frequently a straight line approx...,
It is often possible to write an ...
4  cards
Linear Cost and Revenue Functions (3.11.2)
Linear functions can be used to m...,
Linear functions are applicable t...
2  cards
Graphing Some Important Functions (3.12.1)
This lecture presents some basic ...,
Consider the equation f x cevery ...,
Remember absolute value is always...
3  cards
Graphing Piecewise-Defined Functions (3.12.2)
Piecewise functions are those tha...,
Piecewise functions can have diff...
2  cards
Matching Equations with Their Graphs (3.12.3)
Each type of equation has its own...,
Ten basic types of equations are ...,
Y 1 x y is equal to 1 divided by ...
8  cards
The Greatest Integer Function (3.13.1)
The greatest integer function loo...,
The graph of this function is som...,
Here are some examples that satis...
3  cards
Graphing the Greatest Integer Function (3.13.2)
The greatest integer function loo...,
The graph of this function is som...,
The greatest integer brackets sho...
3  cards
Deconstructing the Graph of a Quadratic Function (3.14.1)
Quadratic functions 1 represent p...,
The domain for quadratic function...,
Your function is f x x 3 2 4 so y...
3  cards
Nice-Looking Parabolas (3.14.2)
Standard form of a parabola f x a...,
Vertex of a parabola h k h b 2a k...,
Standard form for parabola showin...
6  cards
Using the Discriminant to Graph Parabolas (3.14.3)
Quadratic equation ax 2 bx c 0,
Discriminant b2 4ac checking the ...,
Analyzing the discriminant gives ...
3  cards
Maximum Height in the Real World (3.14.4)
Standard form of a parabola f x a...,
In this example your x axis repre...
2  cards
Finding the Vertex by Completing the Square (3.15.1)
Standard form of a quadratic func...,
Completing the square is one meth...,
In this example the x terms are x...
3  cards
Using the Vertex to Write the Quadratic Equation (3.15.2)
Standard form of a quadratic func...,
To write a quadratic equation in ...,
One way to determine the vertex h...
3  cards
Finding the Maximum or Minimum of a Quadratic (3.15.3)
Every parabola has a turning poin...,
On a parabola opening along the y...,
This parabola is positive it will...
4  cards
Graphing Parabolas (3.15.4)
Standard form of a quadratic func...,
To write a quadratic equation in ...,
This example is for a negative pa...
8  cards
Shifting Curves along Axes (3.16.1)
Shifting a graph up is a matter o...,
Shifting a graph to the left on t...,
Symmetry means that half the grap...
6  cards
Shifting or Translating Curves along Axes (3.16.2)
Shifting up or down on a graph is...,
Shifting sideways on a graph is a...,
Shift carefully when you add to y...
4  cards
Stretching a Graph (3.16.3)
Multiplying the equation of a qua...,
Multiplying the equation of a qua...
2  cards
Graphing Quadratics Using Patterns (3.16.4)
To graph any function follow thes...,
Your first step is to graph the g...
2  cards
Determining Symmetry (3.17.1)
Symmetry indicates that half the ...,
An even function is one which exa...,
An even function will pair each y...
6  cards
Reflections (3.17.2)
Reflecting a curve over the x axi...,
Reflecting a curve over the y axi...
2  cards
Reflecting Specific Functions (3.17.3)
Reflecting over the x axis means ...,
Reflecting over the y axis means ...,
When reflecting a function across...
4  cards
Using Operations on Functions (3.18.1)
Using operations with functions i...,
All four of the basic operations ...,
Remember to watch signs carefully
4  cards
Composite Functions (3.18.2)
A composite function is made up o...,
The benefit of composing function...,
Composition notation indicates th...
5  cards
Components of Composite Functions (3.18.3)
The benefit of composing function...,
Composition notation indicates th...,
Note carefully which function is ...
4  cards
Finding Functions That Form a Given Composite (3.18.4)
The benefit of composing function...,
Composition notation f g indicate...,
Note carefully which function is ...
4  cards
Finding the Difference Quotient of a Function (3.18.5)
Difference quotient d x f x h f x h,
This example shows how the differ...
2  cards
Using Long Division with Polynomials (4.1.1)
Division for polynomials follows ...,
When setting up your polynomial d...,
Your remainder is always less tha...
4  cards
Long Division: Another Example (4.1.2)
When you see a rational expressio...,
Division with polynomials is very...,
Be careful to match like terms wh...
4  cards
Using Synthetic Division with Polynomials (4.2.1)
Synthetic division is a shorthand...,
Synthetic division only works whe...,
To set up the problem change the ...
4  cards
More Synthetic Division (4.2.2)
Synthetic division only works whe...,
To set up the problem change the ...,
Be sure that the coefficients mat...
3  cards
The Remainder Theorem (4.3.1)
The remainder theorem if a polyno...,
This theorem and synthetic divisi...,
The remainder will always have le...
4  cards
More on the Remainder Theorem (4.3.2)
The remainder theorem if a polyno...,
This theorem and synthetic divisi...,
The remainder will always have le...
4  cards
The Factor Theorem and Its Uses (4.4.1)
The factor theorem says x c must ...,
The remainder theorem says that f...,
Synthetic division only works whe...
3  cards
Factoring a Polynomial Given a Zero (4.4.2)
A zero of a polynomial is a point...,
The factor theorem states that x ...
2  cards
Presenting the Rational Zero Theorem (4.5.1)
A rational number is a fraction a...,
If the polynomial has integer coe...,
The rational zero theorem says th...
4  cards
Considering Possible Solutions (4.5.2)
If the polynomial has integer coe...,
Any function of degree n will hav...
2  cards
Finding Polynomials Given Zeros, Degree, and One Point (4.6.1)
The factor theorem states that x ...,
A real zero of a polynomial is a ...,
Given three zeroes and one point ...
3  cards
Finding all Zeros and Multiplicities of a Polynomial (4.6.2)
A real zero or root is a point wh...,
Multiplicity of a zero is the num...,
A curve which just touches the x ...
3  cards
Finding the Real Zeros for a Polynomial (4.6.3)
The factor theorem says x c must ...,
A real zero or root is a point wh...,
Difference of two cubes x 3 y 3 x...
3  cards
Using Descartes' Rule of Signs (4.6.4)
Rene descartes 1596 1650 was sign...,
Descartes rule of signs informs u...,
The number of real number zeros t...
3  cards
Finding the Zeros of a Polynomial from Start to Finish (4.6.5)
The factor theorem says that x c ...,
Finding all the zeros of a polyno...,
Every rational integral function ...
4  cards
Matching Graphs to Polynomial Functions (4.7.1)
Rational root theorem given f x a...,
The rational root theorem is very...,
When graphing polynomials every m...
4  cards
Sketching the Graphs of Basic Polynomial Functions (4.7.2)
Graphs of polynomials with even d...,
Graphs of polynomials with odd de...,
For the graphs of y x 2 y x 4 y x...
4  cards
Understanding Rational Functions (4.8.1)
Rational functions are quotients ...,
An asymptote is a line that the g...
2  cards
Basic Rational Functions (4.8.2)
Rational functions are quotients ...,
An asymptote is a line that the g...
2  cards
Vertical Asymptotes (4.9.1)
A vertical asymptote is a vertica...,
To find the vertical asymptotes o...
2  cards
Horizontal Asymptotes (4.9.2)
A horizontal asymptote is a horiz...,
To find the horizontal asymptotes...
2  cards
Graphing Rational Functions (4.9.3)
An asymptote is a line that the g...,
You can use the horizontal and ve...
2  cards
Graphing Rational Functions: More Examples (4.9.4)
An asymptote is a line that the g...,
You can use the horizontal and ve...
2  cards
Oblique Asymptotes (4.9.5)
An asymptote is a line that the g...,
An oblique asymptote is an asympt...,
If a rational function is equival...
3  cards
Oblique Asymptotes: Another Example (4.9.6)
An oblique asymptote is an asympt...,
The graph of a rational function ...
2  cards
Understanding Inverse Functions (5.1.1)
An inverse function undoes anothe...,
An inverse function reverses the ...,
Not all functions have inverse fu...
4  cards
The Horizontal Line Test (5.1.2)
The horizontal line test if the g...,
A one to one function is a functi...
2  cards
Are Two Functions Inverses of Each Other? (5.1.3)
The graphs of inverse functions a...,
The notation means the inverse of...,
Inverse functions satisfy the two...
3  cards
Graphing the Inverse (5.1.4)
The horizontal line test says tha...,
The graph of the inverse of a fun...,
To reflect the graph of a functio...
3  cards
Finding the Inverse of a Function (5.2.1)
To find the inverse of a function...
1  cards
Finding the Inverse of a Function with Higher Powers (5.2.2)
To find the inverse of a function...
1  cards
An Introduction to Exponential Functions (5.3.1)
Exponential functions are functio...
1  cards
Graphing Exponential Functions: Useful Patterns (5.3.2)
Exponential functions are functio...,
The graphs of exponential functio...,
The larger the base of an exponen...
3  cards
Graphing Exponential Functions: More Examples (5.3.3)
Exponential functions are functio...,
You can graph many exponential fu...,
The base of an exponential functi...
3  cards
Using Properties of Exponents to Solve Exponential Equations (5.4.1)
Exponential equations are equatio...,
Steps for solving an exponential ...,
Review of the properties of expon...
3  cards
Finding Present Value and Future Value (5.4.2)
The value of an investment over t...,
The compound interest formula a p...,
You can use the compound interest...
3  cards
Finding an Interest Rate to Match Given Goals (5.4.3)
The value of an investment over t...,
The compound interest formula a p...,
You can use the compound interest...
3  cards
e (5.5.1)
The number e is approximately equ...,
The number e is very important fo...
2  cards
Applying Exponential Functions (5.5.2)
The number e is approximately equ...,
The number e is very important fo...,
The population of the world can b...
3  cards
An Introduction to Logarithmic Functions (5.6.1)
Logarithms and exponential functi...,
A log is an exponent the statemen...,
A log written without a b value i...
3  cards
Converting between Exponential and Logarithmic Functions (5.6.2)
When converting from logarithmic ...,
A log written without a b value i...
2  cards
Finding the Value of a Logarithmic Function (5.7.1)
When calculating logs think of th...,
A log written without a b value i...
2  cards
Solving for x in Logarithmic Equations (5.7.2)
When solving logarithmic equation...,
A log written without a b value i...
2  cards
Graphing Logarithmic Functions (5.7.3)
Graphs of logarithmic functions a...
1  cards
Matching Logarithmic Functions with Their Graphs (5.7.4)
Since all logarithmic functions h...
1  cards
Properties of Logarithms (5.8.1)
The properties of logarithms foll...,
Remember a log is an exponent,
A log written without a b value i...
3  cards
Expanding a Logarithmic Expression Using Properties (5.8.2)
To simplify logs expand them out ...,
A log written without a b value i...
2  cards
Combining Logarithmic Expressions (5.8.3)
To combine logarithms use their p...,
A common logarithm is one with no...,
A natural logarithm ln has e as i...
4  cards
Evaluating Logarithmic Functions Using a Calculator (5.9.1)
When using a calculator to find t...,
A log written without a b value i...
2  cards
Using the Change of Base Formula (5.9.2)
The change of base formula log b ...,
When a log has a base different f...,
A log written without a b value i...
3  cards
The Richter Scale (5.10.1)
The richter scale formula r log i...
1  cards
The Distance Modulus Formula (5.10.2)
The distance modulus formula m 5 ...,
The variables in the distance mod...,
The distance modulus formula is u...
3  cards
Solving Exponential Equations (5.11.1)
When solving for variables in the...
1  cards
Solving Logarithmic Equations (5.11.2)
When solving an equation made up ...,
Always check your answers for ext...
2  cards
Solving Equations with Logarithmic Exponents (5.11.3)
When working with equations with ...
1  cards
Compound Interest (5.12.1)
The compound interest formula a p...
1  cards
Predicting Change (5.12.2)
When working with equations with ...
1  cards
An Introduction to Exponential Growth and Decay (5.13.1)
Population growth is one example ...,
When working with exponential fun...
2  cards
Half-Life (5.13.2)
The half life of a substance is t...
1  cards
Newton's Law of Cooling (5.13.3)
Exponential and logarithmic equat...,
Newton s law of cooling t t a t0 ...
2  cards
Continuously Compounded Interest (5.13.4)
Another real world application of...,
Continuously compounded interest ...
2  cards
Finding the Quadrant in Which an Angle Lies (6.1.1)
Angles are measured from the posi...,
The plane is split into four regi...,
Acute angles measure between 0 an...
7  cards
Finding Coterminal Angles (6.1.2)
Review coterminal angles are angl...,
The measures of coterminal angles...
2  cards
Finding the Complement and Supplement of an Angle (6.1.3)
Two positive angles are complemen...,
Two positive angles are supplemen...
2  cards
Converting between Degrees and Radians (6.1.4)
Mathematicians prefer to measure ...,
Use the conversion 2 radians 360 ...
2  cards
Using the Arc Length Formula (6.1.5)
The arc length of an arc of a cir...
1  cards
An Introduction to the Trigonometric Functions (6.2.1)
The trigonometric functions of an...,
The three basic trig functions ar...,
Every angle can be expressed in r...
3  cards
Evaluating Trigonometric Functions for an Angle in a Right Triangle (6.2.2)
Use the pythagorean theorem to fi...,
When given the value of a trig fu...
2  cards
Finding an Angle Given the Value of a Trigonometric Function (6.2.3)
You can sometimes find the measur...
1  cards
Using Trigonometric Functions to Find Unknown Sides of Right Triangles (6.2.4)
You can use trigonometry to solve...
1  cards
Finding the Height of a Building (6.2.5)
Review you can use trigonometry t...,
Trigonometry has many real world ...
2  cards
Evaluating Trigonometric Functions for an Angle in the Coordinate Plane (6.3.1)
If x y is a point on the terminal...,
For angles in quadrant i all trig...
2  cards
Evaluating Trigonometric Functions Using the Reference Angle (6.3.2)
The reference angle for an angle ...,
To find the value of a trig funct...
2  cards
Finding the Value of Trigonometric Functions Given Information about the Values of Other Trigonometric Functions (6.3.3)
It is possible to find the value ...
1  cards
Trigonometric Functions of Important Angles (6.3.4)
Memorize the trigonometric functi...
1  cards
An Introduction to the Graphs of Sine and Cosine Functions (6.4.1)
The graph of the sine function os...,
The amplitude of an oscillating f...,
The period of an oscillating func...
3  cards
Graphing Sine or Cosine Functions with Different Coefficients (6.4.2)
The coefficients in the functions...,
The amplitude of the function y a...,
The period of the function y sin ...
3  cards
Finding Maximum and Minimum Values and Zeros of Sine and Cosine (6.4.3)
When graphing trigonometric funct...,
Adding or subtracting a constant ...
2  cards
Solving Word Problems Involving Sine or Cosine Functions (6.4.4)
One application of the sine or co...
1  cards
Graphing Sine and Cosine Functions with Phase Shifts (6.5.1)
A phase shift is a horizontal tra...
1  cards
Fancy Graphing: Changes in Period, Amplitude, Vertical Shift, and Phase Shift (6.5.2)
Review use information about the ...
1  cards
Graphing the Tangent, Secant, Cosecant, and Cotangent Functions (6.6.1)
The tangent secant cosecant and c...
1  cards
Fancy Graphing: Tangent, Secant, Cosecant, and Cotangent (6.6.2)
Graph tangent secant cosecant and...
1  cards
Identifying a Trigonometric Function from its Graph (6.6.3)
To identify which trig function a...
1  cards
An Introduction to Inverse Trigonometric Functions (6.7.1)
Review in order for a function f ...,
The basic trigonometric functions...
2  cards
Evaluating Inverse Trigonometric Functions (6.7.2)
When evaluating an inverse trigon...
1  cards
Solving an Equation Involving an Inverse Trigonometric Function (6.7.3)
To solve an equation containing a...
1  cards
Evaluating the Composition of a Trigonometric Function and Its Inverse (6.7.4)
To evaluate a composite trigonome...,
Always consider the range of the ...
2  cards
Applying Trigonometric Functions: Is He Speeding? (6.7.5)
An angle of depression is the ang...,
An angle of elevation is the angl...,
The angle of depression looking d...
5  cards
Fundamental Trigonometric Identities (7.1.1)
An identity is an equation that i...,
Four basic trigonometric identiti...
2  cards
Finding All Function Values (7.1.2)
Four basic trigonometric identiti...,
Given the value of a trigonometri...
2  cards
Simplifying a Trigonometric Expression Using Trigonometric Identities (7.2.1)
Four basic trigonometric identiti...,
You can use trigonometric identit...,
Writing a trigonometric function ...
3  cards
Simplifying Trigonometric Expressions Involving Fractions (7.2.2)
Four basic trigonometric identiti...,
Review you can use trigonometric ...,
Review writing a trig function in...
3  cards
Simplifying Products of Binomials Involving Trigonometric Functions (7.2.3)
Four basic trigonometric identiti...,
To simplify a product of trigonom...,
Review rewriting expressions in t...
3  cards
Factoring Trigonometric Expressions (7.2.4)
Four basic trigonometric identiti...,
Trigonometric expressions can be ...,
Review rewriting expressions in t...
3  cards
Determining Whether a Trigonometric Function Is Odd, Even, or Neither (7.2.5)
Review a function f x is odd if f...,
The sine and tangent functions ar...
2  cards
Proving an Identity (7.3.1)
Review an identity is a mathemati...,
When proving an identity treat ea...
2  cards
Proving an Identity: Other Examples (7.3.2)
Review an identity is a mathemati...,
Review when proving an identity t...
2  cards
Solving Trigonometric Equations (7.4.1)
Since trig functions are periodic...
1  cards
Solving Trigonometric Equations by Factoring (7.4.2)
When solving trig equations by fa...,
Review since trig functions are p...
2  cards
Solving Trigonometric Equations with Coefficients in the Argument (7.4.3)
A coefficient in the argument of ...
1  cards
Solving Trigonometric Equations Using the Quadratic Formula (7.4.4)
Some quadratic trigonometric equa...,
Review coefficients in the argume...,
Review since trig functions are p...
3  cards
Solving Word Problems Involving Trigonometric Equations (7.4.5)
One application of the trig funct...,
Review since trig functions are p...
2  cards
Identities for Sums and Differences of Angles (7.5.1)
The sum and difference identities...
1  cards
Using Sum and Difference Identities (7.5.2)
When finding trigonometric functi...,
The sine of a difference of angle...
2  cards
Using Sum and Difference Identities to Simplify an Expression (7.5.3)
Sum and difference identities can...,
The sum and difference identities...
2  cards
Confirming a Double-Angle Identity (7.6.1)
The double angle identities arise...,
The double angle identities sin 2...
2  cards
Using Double-Angle Identities (7.6.2)
Double angle identities can help ...,
The double angle identities sin 2...
2  cards
Solving Word Problems Involving Multiple-Angle Identities (7.6.3)
Multiple angle identities involve...,
Trigonometry has many practical a...,
Review area of a rectangle base h...
5  cards
Using a Cofunction Identity (7.7.1)
The cofunction identities relate ...
1  cards
Using a Power-Reducing Identity (7.7.2)
Power reducing identities allow y...,
The power reducing identities cos...
2  cards
Using Half-Angle Identities to Solve a Trigonometric Equation (7.7.3)
Half angle identities allow you t...
1  cards
The Law of Sines (8.1.1)
The law of sines allows you to so...,
In a triangle with sides a b and ...
2  cards
Solving a Triangle Given Two Sides and One Angle (8.1.2)
Review the law of sines solves fo...,
Review the law of sines sin a a s...
2  cards
Solving a Triangle (SAS): Another Example (8.1.3)
Review the law of sines sin a a s...,
If the side opposite the given an...
2  cards
The Law of Sines: An Application (8.1.4)
Review the law of sines sin a a s...
1  cards
The Law of Cosines (8.2.1)
Like the law of sines the law of ...,
The law of cosines is used to sol...,
The law of cosines has three form...
3  cards
The Law of Cosines (SSS) (8.2.2)
Review the law of cosines has thr...,
Review the law of cosines is used...,
Review the law of sines sin a a s...
3  cards
The Law of Cosines (SAS): An Application (8.2.3)
Review the law of cosines has thr...,
Review the law of cosines is used...,
Review the law of sines sin a a s...
3  cards
Heron's Formula (8.2.4)
To find the area of any triangle ...,
Heron s formula has two parts for...
2  cards
An Introduction to Vectors (8.3.1)
A vector is a mathematical object...
1  cards
Finding the Magnitude and Direction of a Vector (8.3.2)
The magnitude of a vector is its ...,
The magnitude of a vector is its ...
2  cards
Vector Addition and Scalar Multiplication (8.3.3)
A number that is multiplied into ...,
Scalar multiplication can change ...,
The process of adding two vectors...
3  cards
Finding the Components of a Vector (8.4.1)
When given a vector s magnitude a...
1  cards
Finding a Unit Vector (8.4.2)
A unit vector is a vector with a ...,
The unit vector in the direction ...
2  cards
Solving Word Problems Involving Velocity or Forces (8.4.3)
Velocity can be expressed as a di...,
Degree measure starts at the posi...
2  cards
Graphing a Complex Number and Finding Its Absolute Value (8.5.1)
Review a complex number x yi has ...,
Complex numbers can be graphed in...,
The absolute value or modulus of ...
3  cards
Expressing a Complex Number in Trigonometric or Polar Form (8.5.2)
To express a complex number z in ...,
Review the standard form of a com...
2  cards
Multiplying and Dividing Complex Numbers in Trigonometric or Polar Form (8.5.3)
To multiply two complex numbers s...,
Divide the r terms and subtract t...
2  cards
Using DeMoivre's Theorem to Raise a Complex Number to a Power (8.6.1)
Review a complex number in polar ...,
You can raise a complex number z ...
2  cards
Roots of Complex Numbers (8.6.2)
Review a complex number in polar ...,
You can raise a complex number z ...,
Also use demoivre s theorem to fi...
3  cards
More Roots of Complex Numbers (8.6.3)
Also use demoivre s theorem to fi...,
Review complex roots always come ...
2  cards
Roots of Unity (8.6.4)
Also use demoivre s theorem to fi...,
The roots of unity are the comple...
2  cards
An Introduction to Polar Coordinates (8.7.1)
Instead of describing points usin...,
In polar coordinates a point is s...
2  cards
Converting between Polar and Rectangular Coordinates (8.7.2)
To convert from polar coordinates...,
To convert from rectangular coord...
2  cards
Converting between Polar and Rectangular Equations (8.7.3)
The polar transformation equation...
1  cards
Graphing Simple Polar Equations (8.7.4)
When graphing in polar coordinate...,
To graph a polar equation first c...
2  cards
Graphing Special Polar Equations (8.7.5)
General polar equation of a circl...
1  cards
An Introduction to Linear Systems (9.1.1)
A system of equations means that ...,
The number of times that the grap...
2  cards
Solving a System by Substitution (9.1.2)
The substitution method is one wa...,
Finding the solutions to a linear...
2  cards
Solving a System by Elimination (9.1.3)
The elimination method is another...,
In the elimination method start b...
2  cards
An Introduction to Linear Systems in Three Variables (9.2.1)
The set of points satisfying a li...,
The set of points satisfying a sy...
2  cards
Solving Linear Systems in Three Variables (9.2.2)
You can solve a system of three l...,
An independent system of three eq...,
A dependent system of three equat...
4  cards
Solving Inconsistent Systems (9.2.3)
You can solve a system of three e...,
An inconsistent system of three e...
2  cards
Solving Dependent Systems (9.2.4)
You can solve a system of three e...,
A dependent system of three equat...,
A system of equations can be cons...
3  cards
Solving Systems with Two Equations (9.2.5)
When solving a system of two equa...,
You can solve a system of two equ...
2  cards
Investments (9.3.1)
You can use systems of linear equ...
1  cards
Solving with Partial Fractions (9.3.2)
You can use the technique of part...,
Partial fractions help you work b...
2  cards
Solving Nonlinear Systems Using Elimination (9.4.1)
Linear equations only involve var...,
Equations that are not linear are...
2  cards
Solving Nonlinear Systems by Substitution (9.4.2)
Nonlinear equations can involve s...
1  cards
An Introduction to Matrices (9.5.1)
A matrix is a rectangular block o...,
The numbers in a matrix are calle...,
Systems of linear equations can b...
4  cards
The Arithmetic of Matrices (9.5.2)
To add or subtract matrices they ...,
Remember to use signs properly es...
2  cards
Multiplying Matrices by a Scalar (9.5.3)
A scalar is a single element a nu...,
Scalar multiplication of a matrix...,
You can add and subtract matrices...
3  cards
Multiplying Matrices (9.5.4)
To successfully multiply two matr...,
It is possible that one matrix ca...,
The dimension of a matrix is refe...
4  cards
Using the Gauss-Jordan Method (9.6.1)
The gauss jordan method uses matr...,
When using the gauss jordan metho...,
An augmented matrix is a matrix r...
3  cards
Using Gauss-Jordan: Another Example (9.6.2)
The gauss jordan method uses matr...,
When using the gauss jordan metho...
2  cards
Evaluating 2x2 Determinants (9.7.1)
A determinant is a number associa...,
A square matrix has the same numb...,
The numbers in a matrix are calle...
7  cards
Evaluating nxn Determinants (9.7.2)
A determinant is a number associa...,
A square matrix has the same numb...,
Determinant notation det a or a w...
4  cards
Finding a Determinant using Expanding by Cofactors (9.7.3)
The numbers in a matrix are calle...,
A minor of a square matrix a 3x3 ...,
A cofactor is a minor multiplied ...
3  cards
Applying Determinants (9.7.4)
Determinants can be used to calcu...,
Three or more points are collinea...
2  cards
Using Cramer's Rule (9.8.1)
Cramer s rule states that determi...,
Solving for x means using the det...,
Solving for y means using the det...
3  cards
Using Cramer's Rule in a 3x3 Matrix (9.8.2)
Cramer s rule states that determi...,
The solution for any variable a i...
2  cards
An Introduction to Inverses (9.9.1)
The multiplicative identity of an...,
The multiplicative inverse of any...,
The identity matrix is the one th...
4  cards
Inverses: 2x2 Matrices (9.9.2)
An inverse matrix is one that whe...,
The only matrices that have inver...,
To check whether one matrix is th...
4  cards
Another Look at 2x2 Inverses (9.9.3)
An inverse matrix is one that whe...,
The only matrices that have inver...,
To check whether one matrix is th...
4  cards
Inverses: 3x3 Matrices (9.9.4)
A 3x3 matrix is an array with thr...,
An inverse matrix is one that whe...,
The only matrices that have inver...
5  cards
Solving a System of Equations with Inverses (9.9.5)
An inverse matrix is one that whe...,
The only matrices that have inver...,
The inverse of a 2x2 matrix a a b...
3  cards
An Introduction to Graphing Linear Inequalities (9.10.1)
A system of inequalities means th...,
When graphing inequalities start ...
2  cards
Graphing Linear and Nonlinear Inequalities (9.10.2)
When graphing inequalities start ...
1  cards
Graphing the Solution Set of a System of Inequalities (9.10.3)
Systems of inequalities might div...
1  cards
Solving for Maxima-Minima (9.11.1)
Using linear programming you can ...,
To do so graph the system of ineq...
2  cards
Applying Linear Programming (9.11.2)
Review using linear programming y...
1  cards
An Introduction to Conic Sections (10.1.1)
A conic section is a curve made b...
1  cards
An Introduction to Parabolas (10.1.2)
A parabola consists of the set of...
1  cards
Determining Information about a Parabola from Its Equation (10.1.3)
A parabola consists of the set of...,
A parabola of the form y cx 2 has...
2  cards
Writing an Equation for a Parabola (10.1.4)
A parabola consists of the set of...,
The vertex of a parabola is the p...,
A parabola with vertex at h k and...
3  cards
An Introduction to Ellipses (10.2.1)
An ellipse consists of the set of...,
The standard equation for an elli...,
The standard equation for an elli...
4  cards
Finding the Equation for an Ellipse (10.2.2)
An ellipse consists of the set of...,
The standard equation for an elli...
2  cards
Applying Ellipses: Satellites (10.2.3)
The standard equation for an elli...
1  cards
An Introduction to Hyperbolas (10.3.1)
A hyperbola consists of the set o...,
The standard equation for a hyper...,
The standard equation for a hyper...
5  cards
Finding the Equation for a Hyperbola (10.3.2)
The standard equation for a hyper...,
The standard equation for a hyper...,
In either case the hyperbola has ...
3  cards
Applying Hyperbolas: Navigation (10.3.3)
Hyperbolas are useful in many rea...,
The standard equation for a hyper...,
The standard equation for a hyper...
4  cards
Identifying a Conic (10.4.1)
You can determine whether an equa...,
A parabola with vertex at h k and...,
The standard equation for an elli...
4  cards
Name that Conic (10.4.2)
You can determine whether an equa...,
A parabola with vertex at h k and...,
The standard equation for an elli...
4  cards
Rotation of Axes (10.4.3)
A rotation of axes is a rotation ...,
The angle of rotation is the angl...,
The xy axes can be rotated to gra...
3  cards
Rotating Conics (10.4.4)
The general equation of a conic w...,
The general equation of a conic w...,
If the equation of a conic includ...
4  cards
Using the Binomial Theorem (10.5.1)
Pascals triangle is a group of nu...,
The binomial theorem can be used ...,
The binomial theorem states that ...
3  cards
Binomial Coefficients (10.5.2)
A factorial of a natural number n...,
The binomial theorem can be used ...
2  cards
Finding a Term of a Binomial Expression (10.5.3)
A power of a binomial such as x y...
1  cards
Understanding Sequence Problems (10.6.1)
A sequence is an ordered collecti...,
An inductive sequence uses a patt...,
The fibonacci sequence a1 1 a2 1 ...
3  cards
Solving Problems Involving Arithmetic Sequences (10.6.2)
An arithmetical sequence is a seq...,
Arithmetical sequences follow the...
2  cards
Solving Problems Involving Geometric Sequences (10.6.3)
A geometric sequence is a sequenc...
1  cards
Proving Formulas Using Mathematical Induction (10.7.1)
Mathematical induction is a way o...
1  cards
Examples of Induction (10.7.2)
When proving something by mathema...
1  cards
Solving Problems Involving Permutations (10.8.1)
Probability is a mathematical mea...,
A permutation is a way of arrangi...,
The permutation formula p n r n n r
3  cards
Solving Problems Involving Combinations (10.8.2)
A combination is a way of selecti...,
The combination formula c n r n r...
2  cards
Independent Events (10.8.3)
Probability is defined as the rat...,
Events are independent events whe...
2  cards
Inclusive and Exclusive Events (10.8.4)
Review probability is defined as ...,
Events are inclusive events when ...,
Events are exclusive events when ...
3  cards

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