 # Functions and Graphs

## Vocabulary

### compression

transformation that moves each point of a graph closer to the $x$- or $y$-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 $y$-values decrease as the $x$-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 $y$-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 $y$-values increase as the $x$-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 $x$- or $y$-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.