Functions and Graphs

Vocabulary

compression

transformation that moves each point of a graph closer to the xx- or yy-axis by a scale factor that is between zero and 1

constant function

function with all the same output values

decreasing function

function in which the yy-values decrease as the xx-values increase

domain of a function

set of the first coordinates of the ordered pairs in a function

domain of a relation

set of the first coordinates of the ordered pairs in a relation

even function

function with a graph that is symmetric with respect to the yy-axis

function

relation in which each element of the domain corresponds to exactly one element of the range

global maximum

point where the value of a function is greatest

global minimum

point where the value of a function is least

increasing function

function in which the yy-values increase as the xx-values increase

input

value in the domain of a function

local maximum

turning point where a graph changes from increasing to decreasing

local minimum

turning point where a graph changes from decreasing to increasing

maximum value

greatest value in the range of a function

minimum value

least value in the range of a function

odd function

function with a graph that is symmetric with respect to the origin

output

value in the range of a function

parent function

function from a certain category of functions with the simplest algebraic rule

piecewise function

function that has different rules applied to different intervals in the domain

range of a function

set of the second coordinates of the ordered pairs in a function

range of a relation

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

reflection

transformation in which a graph is flipped across a line

relation

set of ordered pairs

stretch

transformation that moves each point of a graph farther away from the xx- or yy-axis by a scale factor that is greater than 1

transformation

change of the graph of a function

translation

transformation in which a graph is moved vertically or horizontally

turning point

point where a graph changes from increasing to decreasing or from decreasing to increasing

vertical line test

test that uses vertical lines on a graph to determine whether a relation is a function. If any vertical line intersects the graph in more than one point, the graph does not represent a function.