# Graphing Absolute Value Functions

How to graph absolute value functions: examples and their solutions.

## Example 1

Lightly draw *y* = *x*.*x* = 0 makes |*x*| = 0.

So *x* = 0 (*y* axis) is the axis of symmetry.

Use the right side (*x* ≥ 0) of *y* = 2*x* - 3

to draw the left side (*x* < 0) of the graph

under the reflection in *x* = 0.

Reflection in the *y*-axis

## Example 2

Lightly draw *y* = 2*x* - 3.

Slope-intercept form*x* = 0 makes |*x*| = 0.

So *x* = 0 (*y* axis) is the axis of symmetry.

Use the right side (*x* ≥ 0) of *y* = *x*

to draw the left side (*x* < 0) of the graph

under the reflection in *x* = 0.

Reflection in the *y*-axis

## Example 3

Lightly draw *y* = 2*x* - 3.

2*x* - 3 = 0 makes |2*x* - 3| = 0.

So 2*x* - 3 = 0, *x* = 3/2 is the axis of symmetry.

Use the right side (*x* ≥ 3/2) of *y* = 2*x* - 3

to draw the left side (*x* < 3/2) of the graph

under the reflection in *x* = 3/2.

## Example 4

Lightly draw *y* = 2*x* - 3.*y* = 0 makes |*y*| = 0.

So *y* = 0 (*x* axis) is the axis of symmetry.

Use the upper side (*y* ≥ 0) of *y* = 2*x* - 3

to draw the lower side (*y* < 0) of the graph

under the reflection in *y* = 0.

Reflection in the *x*-axis

## Example 5

Lightly draw *y* = 2*x* - 3.*x* = 0, *y* = 0 makes |*x*| = 0, |*y*| = 0.

So draw the graph in the quadrant I. (*x* ≥ 0, *y* ≥ 0)

Use the graph in the quadrant I

to draw the images under the reflections

in the *x*-axis, *y*-axis, and the origin.