Chapter 1: Expressions, Equations, and Functions

Power

An expression of the form xsquared: that whole thing is the __________

simplest form

An expression that has no like terms and no parentheses

Solving

Finding a value for a variable that makes a sentence true

End behavior

describes how the values of a function behave at each end of the graph

equivalent expressions

expressions that have the same value

Exponent

indicates the number of times the base is used as a factor

algebraic expression

A combination of variables, numbers, and at least one operation.

Equation

A mathematical sentence that contains an equals sign.

Term

A number, a variable, or a product or quotient of numbers and variables.

relative maximum

A point on the graph of a function where no other nearby points have a greater y-coordinate.

Relative minimum

A point on the graph of a function where no other nearby points have a lesser y-coordinate.

Substitution Property

A quantity may be substituted for its equal in any expression.

Solution

A replacement value for the variable in an open sentence

ordered pair

A set of numbers or coordinates used to locate any point on a coordinate plane, written in the form (x,y)

Reflexive Property

Any quantity is equal to itself: a = a

Element

Each object or number in a set

Multiplicative Identity

For any number a, the product of a and 1 is a.

Additive Identity

For any number a, the sum of a and 0 is a.

Vertical line test

If any vertical line passes through no more than one point of the graph of a relation, then the relation is a function.

Transitive Property

If one quantity equals a second quantity, and the second quantity equals a third quantity, then the first quantity equals the third quantity. If a=b and b=c, then a=c

Symmetric Property

If one quantity equals a second quantity, then the second quantity equals the first. If a=b, then b=a.

Mapping

Illustrates how each element of the domain is paired with an element in the range.

Product

In an algebraic expression, the result of the quantities being multiplied is called the __________

Base

In an expression of the form x squared, x is the ___________

order of operations

PEMDAS

Like terms

Terms that contain the same variables raised to the same power.

Extrema

The maximum and minimum values of a function

reciprocal

The multiplicative inverse of a number

Commutative Property

The order in which numbers are added or multiplied does not change the sum or product.

Origin

The point where the two axes intersect at their zero points

Multiplicative Property of Zero

The product of any number and zero is zero.

Domain

The set of the first numbers of the ordered pairs in a relation

independent variable

The variable in a function with a value that is subject to choice.

dependent variable

The variable in a relation with a value that depends on the value of the independent variable.

Associative Property

The way in which three or more numbers are grouped when they are added or multiplied does not change their sum or product.

Line symmetry

When a line divides a function on a graph in half and both sides on either side match

Positive

Where the graph lies above the x-axis

Negative

Where the graph lies below the x-axis

Set

a collection of objects or numbers

continuous function

a function graphed with a line or smooth curve

linear function

a function in which the graph of the solutions forms a line

discrete function

a function of points that are not connected

nonlinear function

a function with a graph that is not a straight line

open sentence

a mathematical sentence containing one or more variables

Additive Inverse

a number and its opposite: a+(-a)

Function

a relation in which each element of the domain is paired with exactly one element of the range

Replacement set

a set of numbers from which replacements for a variable may be chosen

Relation

a set of ordered pairs

Distributive Property

a(b + c) = ab + ac

function notation

an equation in the form of 'f(x)=' to show the output value of a function, f, for an input value x

identity

an equation that is true for every value of the variable

Intercept

points where the graph intersects an axis

Factors

quantities being multiplied

Variables

symbols used to represent unspecified numbers or values

x-coordinate

the first number in an ordered pair

coordinate system

the grid formed by the intersection of two number lines, the horizontal axis and the vertical axis

x-axis

the horizontal number line in a coordinate plane

Coefficient

the numerical factor of a term: 6a...6 is the_________

coordinate plane

the plane containing the x and y axis

y-coordinate

the second number in an ordered pair

solution set

the set of elements from the replacement set that make an open sentence true

Range

the set of second numbers of the ordered pairs in a relation

y-axis

the vertical axis on a coordinate plane

x-intercept

the x-coordinate of a point where a graph crosses the x-axis

y-intercept

the y-coordinate of a point where a graph crosses the y-axis

Evaluate

to find the value of an expression

Multiplicative Inverse

two numbers whose product is 1: a/b times b/a =1

Increasing

where the graph goes up

Decreasing

where the graph of the function is going down from left to right