Graph of the absolute value of x

The graph of the absolute value of x is called parent absolute value function. The reason it is given this name is because the absolute value of x is the easiest of all absolute value functions to graph.

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

The vertex of the graph is (-b / m, c)

Using f(x) = |x| we see that, m = 1, b = 0, and c  = 0

You can graph the absolute value of x by looking for the vertex and several other selected points.

First, find the vertex.

The vertex is located at (-b / m , c)

Therefore, the vertex is (-0 / 1, 0) or (0,0)

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

f(1) = |1| = 1

The point is (1,1)

f(-1) = |-1| = 1

The point is (-1,1)

f(2) = |2| = 2

The point is (2,2)

f(-2) = |-2| = 2

The point is (-2,2)

f(3) = |3| = 3

The point is (3,3)

f(-3) = |-3| = 3

The point is (-3,3)

Now, graph the following 7 points: (0,0), (1,1), (-1,1), (2,2), (-2,2), (3,3), and (-3,3)

Things to notice about the graph of the absolute value of x

  • The angle at the vertex is a right angle.
  • The graph is symmetric about the y-axis.
  • The linear "piece" on the right side of the y-axis has a slope of 1 and the linear "piece" on the left side of the y-axis has a slope of -1.
  • The graph is located on both sides of the y-axis, so the domain is all real numbers or (-∞, ∞)
  • The graph is located above the x-axis with the exception of the point (0,0), so the range is all non-negative real numbers or [0, ∞)

Recent Articles

  1. How To Find The Factors Of 20: A Simple Way

    Sep 17, 23 09:46 AM

    Positive factors of 20
    There are many ways to find the factors of 20. A simple way is to...

    Read More

  2. The SAT Math Test: How To Be Prepared To Face It And Survive

    Jun 09, 23 12:04 PM

    SAT math
    The SAT Math section is known for being difficult. But it doesn’t have to be. Learn how to be prepared and complete the section with confidence here.

    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


Math vocabulary quizzes