Lesson 13

Absolute Value Functions (Part 1)

  • Let’s make some guesses and see how good they are.

Problem 1

A group of ten friends played a number guessing game. They were asked to pick a number between 1 and 20. The person closest to the target number wins. The ten people made these guesses:

guess 2 15 10 8 12 19 20 5 7 9
absolute guessing error                    
  1. The actual number was 14. Complete the table with the absolute guessing errors.
  2. Graph the guess and absolute guessing errors.
  3. Is the absolute guessing error a function of the guess? Explain how you know.
Blank coordinate grid, origin O. Horizontal axis, guess, from 0 to 22 by 2’s. Vertical axis, absolute guessing error, from 0 to 20 by 2’s.

Problem 2

Bags of walnuts from a food producer are advertised to weigh 500 grams each. In a certain batch of 20 bags, most bags have an absolute error that is less than 4 grams.

Could this scatter plot represent those 20 bags and their absolute errors? Explain your reasoning.

horizontal axis, weight in grams. vertical axis, absolute error in grams. scatterplot with vertex at 500 comma 0. 

Problem 3

The class guessed how many objects were placed in a mason jar. The graph displays the class results, with an actual number of 47.

20 data points on coordinate grid.

Suppose a mistake was made, and the actual number is 45.

Explain how the graph would change, given the new actual number.

Problem 4

Function \(D\) gives the height of a drone \(t\) seconds after it lifts off.

Sketch a possible graph for this function given that:

  • \(D(3)=4\)
  • \(D(10)=0\)
  • \(D(5)>D(3)\)
Blank grid with axes. Origin O.
(From Unit 4, Lesson 3.)

Problem 5

The population of a city grew from 23,000 in 2010 to 25,000 in 2015. 

  1. What was the average rate of change during this time interval? 
  2. What does the average rate of change tell us about the population growth?
(From Unit 4, Lesson 7.)

Problem 6

Here is the graph of a function.

Which time interval shows the largest rate of change?

Piecewise graph. Horizontal axis, 0 to 8, time, seconds. Vertical axis, 0 to 16, height, feet. Graph starts at 0 comma 9, increases, deceases to 4 comma 0, increases, then flattens out at 6 comma 10.

From 0 to 2 seconds


From 0 to 3 seconds


From 4 to 5 seconds


From 6 to 8 seconds

(From Unit 4, Lesson 7.)

Problem 7

Here are the graphs of \(L(x)\) and \(R(x)\)


Piecce wise function. 


piece wise function.
  1. What are the values of \(L(0)\) and \(R(0)\)?
  2. What are the values of \(L(2)\) and the \(R(2)\)?
  3. For what \(x\)-values is \(L(x)=7\)?
  4. For what \(x\)-values is \(R(x)=7\)?
(From Unit 4, Lesson 12.)

Problem 8

Select all systems that are equivalent to this system of equations: \(\begin {cases} \begin{align} 4x+5y&=1\\x- \hspace{2mm}y&=\frac38 \end{align} \end{cases}\)


\(\begin {cases} \begin{align} 4x+5y&=1\\4x- 4y&=\frac32 \end{align} \end{cases}\)


\(\begin {cases} \begin{align} x+\frac54y&=\frac14\\x- \hspace{2mm}y&=\frac38 \end{align} \end{cases}\)


\(\begin {cases} \begin{align} 4x+5y&=1\\5x- 5y&=3 \end{align} \end{cases}\)


\(\begin {cases} \begin{align} 8x+10y&=2\\8x- \hspace{2mm}8y&=3\end{align} \end{cases}\)


\(\begin {cases} \begin{align} x+y&=\frac15\\x- y&=\frac38 \end{align} \end{cases}\)

(From Unit 2, Lesson 16.)