How to Put An Absolute Value in A Graphing Calculator

Graphing absolute value functions on a calculator is a fundamental skill in algebra and calculus. This guide explains how to enter and visualize absolute value expressions in graphing calculators like TI-84, Desmos, and GeoGebra.

Introduction

The absolute value of a number is its distance from zero on the number line, regardless of direction. The absolute value function is defined as:

f(x) = |x|

Graphing calculators can display this V-shaped graph with its vertex at the origin (0,0). This guide covers how to enter absolute value functions in different calculator models.

Basic Absolute Value Function

To graph the basic absolute value function f(x) = |x|:

Press the Y= button to access the function editor
Enter the function as Y1=abs(X)
Set the window settings: Xmin=-10, Xmax=10, Ymin=-5, Ymax=5
Press GRAPH to view the V-shaped graph

Most graphing calculators use the "abs" function for absolute value. Some models may use "Abs" or "| |" syntax.

Transformed Absolute Value Functions

Absolute value functions can be transformed by shifting, stretching, and reflecting:

f(x) = a|b(x-h)| + k

Where:

a = vertical stretch/compression
b = horizontal stretch/compression
(h,k) = vertex location

Example: To graph f(x) = 2|x-3| + 1:

Enter Y1=2*abs(X-3)+1
Adjust window to view the vertex at (3,1)

Piecewise Absolute Value Functions

Some functions combine absolute value with other expressions:

f(x) = { |x|, x ≤ 0 x², x > 0 }

To enter this in most calculators:

Use the piecewise function feature (often under MATH)
Enter the conditions and corresponding expressions
Graph to see the combined function

FAQ

What is the absolute value symbol on a calculator?: The absolute value symbol is typically represented as "abs" or "| |" depending on the calculator model.
How do I graph absolute value inequalities?: First graph the function, then use the TEST feature to determine where the inequality holds true.
Can I graph absolute value with a square root?: Yes, combine the functions using the calculator's function editor, for example: Y1=abs(√X)
What if my calculator doesn't have an absolute value function?: You can create a piecewise function that returns the positive value for all inputs.
How do I find the vertex of an absolute value graph?: The vertex is at the point where the function changes direction, typically at (h,k) for transformed functions.