Algebra 1: Chapter 3 Vocabulary (copy)

absolute value function

a function that contains an absolute value expression

constant function

a linear equation written in the form y = 0x + b, or y = b

continuous domain

a set of input values that consist of all numbers in an interval

dependent variable

the variable that represents output values of a function

discrete domain

a set of input values that consists of only certain numbers in an interval

domain

the set of all possible input values of a function

family of functions

a group of functions with similar characteristics

function

a relation that pairs each input with exactly one output

function notation

another name for y denoted as f(x) and read as “the value of f at x” or “f of x”

horizontal shrink

a transformation that causes the graph of a function to shrink toward the y-axis when all the x-coordinates are multiplied by a factor a, where a > 1

horizontal stretch

a transformation that causes the graph of a function to stretch away from the y-axis when all the x-coordinates are multiplied by a factor a, where 0 > a > 1

independent variable

the variable that represents the input values of a function

linear equation in two variables

an equation that can be written in the form y = mx + b, where m and b are constants

linear function

a function whose graph is a nonvertical line

nonlinear function

a function that does not have a constant rate of change and whose graph is not a line

parent function

the most basic function in a family of functions

range of a function

the set of all possible output values of a function

reflection

a transformation that flips a graph over a line called the line of reflection

relation

a pairing of inputs with outputs

rise

the change in y between any two points on a line

run

the change in x between any two points on a line

slope

the rate of change between any two points on a line

slope-intercept form

a linear equation written in the form y = mx + b

solution of a linear equation in two variables

an ordered pair (x, y) that makes an equation true

standard form of a linear equation

a linear equation written in the form Ax + By = C, where A, B, and C are real numbers and A and B are both not zero

transformation

a change in the size, shape, position, or orientation of a graph

translation

a transformation that shifts a graph horizontally and/or vertically but does not change the size, shape, or orientation of the graph

vertex

the point where a graph changes direction

vertex form of an absolute value function

an absolute value function written in the form f(x) = a

vertical shrink

a transformation that causes the graph of a function to shrink toward the x-axis when all the y-coordinates are multiplied by a factor a, where 0 < a < 1

vertical stretch

a transformation that causes the graph of a function to stretch away from the x-axis when all the y-coordinates are multiplied by a factor a, where 0 < a < 1

x-intercept

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

y-intercept

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