Graph an absolute value function

You can quickly graph an absolute value function using the vertex and a table of values.

Note that the vertex is the sharp corner of the graph!

Example #1

Graph f(x) = |2x + 6|

The general form of the function is f(x) = |mx + b| + c

Using f(x) = |2x + 6|, m = 2, b = 6, and c  = 0

First, find the vertex.

As seen in the lesson about absolute value function, the vertex is located at (-b / m, c)

Therefore, the vertex is (-6 / 2, 0) or (-3, 0)

Now, evaluate the function for several selected values of x.

x -5 -4 -2 -1 0
f(x) 4 2 2 4 6

The graph of the absolute value function is shown below

Graph of absolute value function

Example #2

Graph f(x) = |-3x + 15| + 1

The general form of the function is f(x) = |mx + b| + c

Using f(x) = |-3x + 15| + 1, m = -3, b = 15, and c  = 1

First, find the vertex.

The vertex is located at (-b / m, c) or (-15 / -3, 1) or (5, 1)

The vertex is (-6 / 2, 0) or (-3, 0)

Now, evaluate the function for several selected values of x.

x 3 4 6 7
f(x) 7 4 4 7

The graph of the absolute value function is shown below

Graph of absolute value function

Recent Articles

  1. Calculate the Conditional Probability using a Contingency Table

    Mar 29, 23 10:19 AM

    Contingency table
    Learn to calculate the conditional probability using a contingency table. This contingency table can help you understand quickly and painlessly.

    Read More

  2. Rational Numbers - Definition and Examples

    Mar 15, 23 07:45 AM

    Rational numbers
    To learn about rational numbers, write their decimal expansion, and recognize rational numbers that are repeating decimals and terminating decimals.

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes

 Recommended

Math vocabulary quizzes