Algebra II Flashcards
A set of ordered pairs can be shown in a ______, _______, _______, or expressed as an ______.
- Graph
- Table of values
- Mapping diagram
- Equation
The set of x-values is called the _______ and the set of y-values is called the _______.
- Domain
- Range
A relation with distinct points is called _______. A relation with connected lines or curvees is called _______.
- Discrete
- Continuous
Rules for domain and range
- Order from least to greatest
- No repeats
- In brackets {}
Function definition and example:
A relation in which each element of the domain is paired with exactly one element of the range.
Function:
{(0, 1),(-5, 2), (6, -2), (5, 7)}
NOT a function:
{(-7, 2), (6, -1), (6, 2), (-3, 9)}
Vertical line test:
In order to be a function, a vertical line cannot pass through more than one point in the relation. (This means the input (x-value) would have more than one output (y-value) and would not satisfy the definition to have one input and one output…(x,y))
Continuous examples:
- For domain, scan your pencil left to right and Identify the x-values in which you are “touching” the graph.
- For range, scan your pencil down and up and identify the y-values in which you are “touching” the graph.
Given:
f(x) = -5x -14
g(x) = -x^2 + 9x -1
h(x) = 5/x + 2
Evaluate:
f(-7) h(1/2) g(-3) f(3) + g(-1)
y = 21 (-7, 21)
y = 2 (1/2, 2)
y = -37 (-3, -37)
y = -40 (3, -40) (-1, -40)
Input, output
When points on a graph lie along a straight line, it is called a _______
linear function
Linear relations can be represented by an _______, for example, the equation of this graph can be written as _______
equations/functions
Standard form: x + y = 8
Slope-intercept form: y = -x + 8
What is the difference between a liner equation and a nonlinear equation?
A linear equation has only x^1 and/or y^1, but not xy, divided x or y’s, x^2 or y^2, or square roots such as nonlinear equations have
A _______ is a function with ordered pairs that satisfy a linear equation. Any linear function can be written in the form f(x) = max + b, where m and b are real numbers
linear function
The point at which the line intersects the x-axis is called _______
The point at which the line intersects the y-axis is called _______
x-intercept
y-intercept
The x-intercept is also referred to as _______, _______, or _______ to the equation
Solutions
Roots
Zeros
To find the x-intercept of an equation, _______ and solve for _______.
To find the y-intercept of an equation, _______ and solve for _______
Cover up y
x
Cover up x
y
x-intercepts and y-intercepts can be written as a _______ or an _______
graph point
equation
To find slope always do _______
vertical or rise first then do horizontal
What is slope in the slope form equation (y = mx + b)?
m
_______a ratio that shows how one variable changes with respect to another.
On a linear graph, this is called the _______ of the line
Fraction/composition
slope
Slope is written as a _______ of the vertical change (_______) to the horizontal change (_______) between any 2 points on a line
This remains _______ for any 2 points of the same line
ratio
y-values
x-values
constant
Slope is written as a _______ in _______. Variable for slope _______.
Fraction
Rise(y)/run(x)
m
Types of slopes:
Positive:
Negative:
Zero:
Undefined:
Rise to the right
Fall to the right
Horizontal line 0/# = 0
Vertical line #/0 = undefined
Slope formula:
m = y2 - y1/x2 - x1
Linear equations are often written in slope-intercept form:
y = mx + b or f(x) = mx + b
(Where m is the slope and b is the y-intercept)
To change from standard form to slope-intercept form?
-A/B or move the A to the other side and divide all of the numbers by the B coefficient
To write a linear equation given the slope of the line (m), and a point that passes through (x1, y1), use the point-slope formula:
y - y1 = m(x - x1)
Slope intercept for undefined is _______
Slope intercept for 0 is _______
x = #
y = #
To write a linear equation given two points (x1, y1) and (x2, y2) use the _______ followed by the _______
Slope formula
Point slope formula
Writing parallel and perpendicular equations. What is this?
Given an equation, you must create another equation that is either parallel or perpendicular to this line, passes through a certain points.
Parallel equations have same slopes
Perpendicular equations have opposite reciprocal slopes
A piecewise function is _______
a function defined by 2 or more equations, or “pieces,” that apply to different parts of the domain.
Piecewise functions’ equations can include linear, absolute value, quadratic, or any other type of function. Therefore, there is no parent function for piecewise functions.
Example: f(x) = {x - 2, if x ≤ 0
{2x + 1, if x > 0
What is a parent function?
the simplest form of any function family, in which it preserves the definition of the entire family.
What is a function?
an equation for which any x that can be plugged into the equation will yield exactly one y out of the equation
What is a function family?
a group of functions with the same degree and that look the same, even with different numbers
An _______ on a graph means that the value is _______, and a _______ means that the value is _______
Open circle
Not included
Closed circle
Included
When there is no value of y, given the x, then it’s _______
undefined
Use a graph to evaluate f (x) given the _______
values
When simplifying radicals, the root applies to every _______
Apply radical rule:
item under the radical
n^√ab = n^√a x n^√b
When graphing linear equations, graph what first?
b
Linear inequality is similar to a linear equation, but _______
uses an inequality symbol
What is the solution to a Linear Inequality
All of the ordered pairs that make the inequality true
