# 7.2: Introducing the Absolute Value Function

**At Grade**Created by: CK-12

*This activity is intended to supplement Algebra I, Chapter 6, Lesson 5.*

In this activity, you will examine data by comparing individual data points to the mean by finding the difference (positive or negative) and the distance from the mean, plot the distances versus the differences to examine the shape of the plot, investigate the absolute value function in the

## Problem 1 - Analyze the Data

The high temperatures in the first twelve days of February were:

Press **STAT ENTER**. Enter these

Press **[MODE]** to return to the home screen. Press **[STAT]** **3:mean**(.

This will paste the command onto the home screen. Press **ENTER** to execute.

Now that you know the mean of the temperatures, press **STAT ENTER** to return to the ‘statistics editor.’ Arrow to the top of

Press

Press **ENTER** to execute. What do you notice about the numbers in

Move over to

Set up a scatter plot to compare the distances to the differences (**1:Plot 1**.

Press **ENTER** to turn the plot **On**. Arrow down to the **Xlist**.

Press **Ylist**. Press

Press **WINDOW**. Set the window as shown.

Press **GRAPH**. Press **TRACE** to examine the relationships between the

When

(sample response:

## Problem 2 - Compare Data Against Equations

Press

Press **GRAPH**. What is the relationship between

Return to

Press **GRAPH**. What is the relationship between

Press **[GRAPH]** to examine the tables for

Return to \begin{align*}Y=\end{align*}. Arrow down to \begin{align*}Y_3\end{align*}. Press **MATH** \begin{align*}\rightarrow\end{align*} to find the absolute value command **1:abs(**. Press **ENTER**. This will paste the command into \begin{align*}Y_3\end{align*}.

Complete the function as shown. Arrow left of \begin{align*}Y_3\end{align*}. Press **ENTER** to change the graph to a ‘thick line.’

Press **GRAPH**. What is the relationship between \begin{align*}y = abs(x)\end{align*} and the scatter plot? NOTE: In your textbook this function will be written as \begin{align*}y = \left | x \right |\end{align*}.

Press \begin{align*}2^{nd}\end{align*} **[GRAPH]** to examine the tables. How are the values for \begin{align*}Y_3\end{align*} related to \begin{align*}Y_1\end{align*} and \begin{align*}Y_2\end{align*}? Where is \begin{align*}Y\end{align*} equal to zero?

## Extension

Examine another absolute value equation. First, clear all earlier functions in \begin{align*}Y=\end{align*} and enter \begin{align*}y = x+7\end{align*} into \begin{align*}Y1\end{align*}. To clear functions, put cursor over the equals sign and press **[CLEAR]**.

Press \begin{align*}2^{nd}\end{align*} **[GRAPH]** Examine the table. When are the \begin{align*}Y_1\end{align*} values positive? When are they negative? When is \begin{align*}Y_1\end{align*} zero?

Return to \begin{align*}Y=\end{align*}. Enter the equation \begin{align*}y = abs(x) + 7\end{align*} into \begin{align*}Y_2\end{align*} using **[MATH]** \begin{align*}\rightarrow\end{align*} abs(Examine the graph. What seems to be the relationship between the graphs?

Examine the table. Is the relationship between \begin{align*}Y_2\end{align*} and \begin{align*}Y_1\end{align*} what you were expecting? Why or why not? Where are the \begin{align*}Y\end{align*} values equal to zero?

Return to \begin{align*}Y=\end{align*}. Enter the equation \begin{align*}y = abs(x + 7)\end{align*} into \begin{align*}Y_2\end{align*} as shown.

Examine the graph. What seems to be the relationship between the graphs? How is this picture different from the graph with \begin{align*}y = abs(x) + 7\end{align*}?

Examine the table. Is the relationship between \begin{align*}Y_2\end{align*} and \begin{align*}Y_1\end{align*} what you were expecting? Why or why not? Where are the \begin{align*}Y\end{align*} values equal to zero?

Compare \begin{align*}y = abs(x) + 7\end{align*} to \begin{align*}y = abs(x + 7)\end{align*}. How are they similar? Different?

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