How to Put Absolute Value Bars in A Graphing Calculator

Introduction

Absolute value functions are widely used in mathematics, engineering, and economics. They appear in equations like distance formulas, optimization problems, and piecewise functions. Graphing these functions accurately requires understanding how to input the absolute value notation into your calculator.

The absolute value of a number x, denoted |x|, is defined as:

This creates a V-shaped graph with its vertex at the origin (0,0) for the basic |x| function.

Absolute Value Basics

Before graphing, understand the basic properties of absolute value functions:

• The graph always forms a V-shape with the vertex at the point where the expression inside the absolute value equals zero
• The slope of the left side of the V is negative, and the slope of the right side is positive
• The function is continuous everywhere
• The minimum value of |x| is always 0

For more complex expressions like |2x-3|, the vertex occurs where 2x-3=0, or x=1.5.

Graphing Absolute Value on a Calculator

Most graphing calculators handle absolute value functions similarly. Here's how to enter them:

TI-84 Series

1. Press [Y=] to access the equation editor
2. Enter your function using the absolute value key [ABS]
3. Example: For |x-2|+3, press [ABS] then (x-2)[)]+3
4. Press [GRAPH] to view the graph

Casio fx-CG50

1. Press [F1] to access the function menu
2. Select "Y=" and enter your function
3. Use the [SHIFT] key to access the absolute value function
4. Press [DRAW] to graph

HP Prime

1. Press [Y=] to edit functions
2. Enter your function using the absolute value notation | |
3. Press [GRAPH] to view

Example: Graphing |x-2|+3

Let's graph the function y = |x-2| + 3 step by step:

Step 1: Identify the vertex

The expression inside the absolute value is x-2. Set it equal to zero:

So the vertex is at x=2. To find the y-coordinate, substitute x=2 into the original equation:

Step 2: Determine the slope

The left side of the V (x < 2) has a slope of -1, and the right side (x > 2) has a slope of 1.

Step 3: Set the window

Adjust your calculator's window settings to view the entire graph:

• Xmin: 0
• Xmax: 4
• Ymin: 0
• Ymax: 6

Step 4: Graph the function

The resulting graph should show a V-shape with the vertex at (2,3).

Common Mistakes to Avoid

When graphing absolute value functions, watch out for these common errors:

1. Incorrect vertex placement

Forgetting to solve the expression inside the absolute value correctly can lead to misplaced vertices.

2. Missing the vertical shift

If your function includes a constant term outside the absolute value (like +3 in |x|+3), don't forget to account for it when finding the vertex.

3. Improper window settings

Choosing window settings that don't show the entire V can make your graph look incomplete.

4. Confusing absolute value with squares

The graph of x² is a parabola, while |x| is a V-shape. These are different functions.

Advanced Techniques

Once you're comfortable with basic absolute value graphs, try these advanced techniques:

1. Graphing piecewise absolute value functions

You can create more complex graphs by combining absolute value functions with other operations.

2. Solving absolute value equations

Use your graphing calculator to visualize and solve equations like |3x-5| = 7.

3. Exploring transformations

Experiment with horizontal and vertical shifts, stretches, and reflections of absolute value functions.

4. Creating absolute value inequalities

Graph inequalities like |x-4| < 2 to visualize the solution set.