Chapter 1 - Vocabulary Flashcards
Algebraic Expression
2x + 3y - 4z
An algebraic expression consists of sums and/or products of numbers and variables
Variables
2x - 3 = 4 The variable would be x
Variables are symbols used to represent unspecified numbers of values.
Term
2x + 4 = .10x
2x, 4, and .10x are terms
Terms of an expression may be a number, a variable, or a product or quotient of numbers or variables.
Factors
In a multiplication equation, the quantities being multiplied are called factors.
Product
The result of multiplying two factors is a product.
Power
An expression like x^n or x to the nth power is called a power. The word power can also refer to an exponent.
Exponent
The exponent indicates the number of times the base is used as a factor.
Base
In an expression in the form x^n, the base is x.
Evaluate
To evaluate an expression, means to find it’s value.
Order of Operations
The rule that lets you know which operation to preform first is called the Order of Operations.
Equivalent Expression
The expressions 4k + 8k and 12k are called equivalent expressions because they represent the same number.
Additive Identity
The sum of any number and 0 is equal to the number. Thus, 0 is called the additive identity.
Multiplicative Identity
Since the product of any number and 1 is equal to the number, 1 is called the multiplicative identity.
Multiplicative Property of Zero
The product of any number and 0 is equal to 0. This is called the Multiplicative Property of Zero.
Multiplicative Inverses
Two numbers whose products is 1 are called Multiplicative Inverses.
Reciprocals
Two numbers whose product is 1 are called multiplicative inverses or reciprocals. 0 has no reciprocals because any number times 0 is 0.
Communicative Property
a + b = b + a
Associative Property
An easy way to find the sum or product of numbers is to group, or associate, the numbers using the Associative Property.
Proof
A proof is a logical argument in which each statement you make is supported by a statement that is accepted as true.
Closure Property
The sum of any two whole numbers is always a whole number. So, the set of whole numbers {0,1,2,3,4,…} is said to be closed under addition. This is an example of the closure property.
Accuracy
Accuracy refers to how close a measured value comes to the actual or desired value.
Distributive Property
a(b + c) = ab + ac
a(b - c) = ab - ac
Symmetric Property of Equality
The Symmetric Property of Equality allows the Distributive Property to be written as follows:
a(b + c) = ab + ac, then ab + ac = a(b + c)
Like Terms
Like Terms are terms that contain the same variables, with corresponding variables having the same power.
Simplest Form
An expression is in simplest form when it contains no like terms or parenthesis.
Coefficient
The coefficient of a term is the numerical factor.
Open Sentence
A mathematical statement that contains algebraic expressions and symbols is an open sentence.
Equation
A sentence that contains an equal sign, =, is an equation.
Solving
Finding a value for a variable that makes a sentence true is called solving.
Solution
The replacement value is a solution.
Replacement Set
A set of numbers from which replacements for a variable may be chosen is called a replacement set.
Set
A set is a collection of objects or numbers that is often shown using braces.
Solution Set
A solution set is the set of elements from the replacement set that make an open sentence true.
Element
Each object or number in the set is called an element.
Identity
An equation that is true for every value of the variable is called an identity.
y-axis
The vertical axis is also called the y-axis.
Coordinate System
A coordinate system is formed by the intersection of two number lines, the horizontal axis and the vertical axis.
Origin
The origin, at (0,0), is the point where the axes intercept.
Coordinate Plane
The plane containing the x- and y-axes is the coordinate plane.
Ordered Pair
Each point is named by an ordered pair.
x-axis
The horizontal axis is also called the x-axis.
y-coordinate
The y-value, called the y-coordinate, represents the vertical placement of the point.
x-coordinate
The x-value, called the x-coordinate, represents the horizontal placement of the point.
Relation
A set of ordered pairs is called a relation. A relation can be represented in several different ways: as an equation, in a graph, with a table, or with a mapping.
Mapping
A mapping illustrates how each element of the domain is paired with an element in the range.
Domain
The set of first numbers of the ordered pairs is the domain.
Range
The set of second numbers of the ordered pairs is the range of the relation.
Independent Variable
In a relation, the value of the variable that determines the output is called the independent variable.
Dependent Variable
The variable with a value that is dependent on the value of the independent variable is called the dependent variable.
Function
A function is a relationship between input and output.
Discrete Function
A graph that consists of points that are not connected is a discrete functions.
Continuous Function
A function graphed with a line or smooth curve is a continuous function.
Vertical Line Test
You can use the vertical line test to see if a graph represents a function. If a vertical line intersects the graph more than once, then the graph is not a function. Otherwise, the relation is a function.
Function Notation
f(x) = 2x - 6
Equation that are functions can be written in a form called function notation.
Equation Function Notation
y = 2x - 6 f(x) = 2x - 6
Nonlinear Function
A function with a graph that is not a straight line is a non-linear function.
Intercepts
The intercepts of a graph are points where the graph intercepts an axis.
y-intercept
The y-coordinate of the point at which the graph intercepts the y-axis is called the y-intercept.
x-intercept
The x-coordinate of the point at which a graph intersects the x-axis is called an x-intercept.
Line Symmetry
A graph possesses line symmetry in the y-axis or some other vertical line of each half of the graph on either side of the line matches exactly.
Postive
A function is positive where it’s graph lies above the x-axis.
Negative
A function is negative where it’s graph lies below the x-axis.
Increasing
A function is increasing where the graph goes up.
Decreasing
A function is decreasing where the graph goes down when viewed from left to right.
Extrema
The points shown are the locations of relatively high or low function values called extrema.
Relative Minimum
A point is a relative minimum if no other nearby points have a lesser y-coordinate.
Relative Maximum
A point is a relative maximum when no other nearby points have a greater y-coordinate.
End Behavior
End behavior describes the values of a function at the positive and negative extremes in it’s domain.
