Graphing Absolute Value Functions

Graphing Absolute Value Functions

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

Example 1

Graph the given function. y = |x|

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 = 2x - 3
to draw the left side (x < 0) of the graph
under the reflection in x = 0.

Reflection in the y-axis

Example 2

Graph the given function. y = 2|x| - 3

Lightly draw y = 2x - 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

Graph the given function. y = |2x - 3|

Lightly draw y = 2x - 3.

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

Use the right side (x ≥ 3/2) of y = 2x - 3
to draw the left side (x < 3/2) of the graph
under the reflection in x = 3/2.

Example 4

Graph the given function. |y| = 2x - 3

Lightly draw y = 2x - 3.

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

Use the upper side (y ≥ 0) of y = 2x - 3
to draw the lower side (y < 0) of the graph
under the reflection in y = 0.

Reflection in the x-axis

Example 5

Graph the given function. |y| = 2|x| - 3

Lightly draw y = 2x - 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.