# Absolute Value Functions (Part 1)

ID: marob-sohus
Illustrative Mathematics, CC BY 4.0
Subject: Algebra, Algebra 2

27 questions

# Absolute Value Functions (Part 1)

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##### 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:

﻿$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \\[-1em] \textbf{guess} & 2 & 15 & 10 & 8 & 12 & 19 & 20 & 5 & 7 & 9 \\[-1em] \\ \hline \\[-1em] \textbf{absolute guessing error} & & & & & & & & & & \\[-1em] \\ \hline \end{array}$﻿

The actual number was 14. Complete the table with the absolute guessing errors. Write the values for the labeled cells in the answer boxes below.

﻿$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \\[-1em] \textbf{guess} & 2 & 15 & 10 & 8 & 12 & 19 & 20 & 5 & 7 & 9 \\[-1em] \\ \hline \\[-1em] \textbf{absolute guessing error} & \text{A} & \text{B} & \text{C} & \text{D} & \text{E} & \text{F} & \text{G} & \text{H} & \text{I} & \text{J} \\[-1em] \\ \hline \end{array}$﻿

1) Cell A

2) Cell B

3) Cell C

4) Cell D

5) Cell E

6) Cell F

7) Cell G

8) Cell H

9) Cell I

10) Cell J

11) Graph the guess and absolute guessing errors.

12) Is the absolute guessing error a function of the guess?

True or false? Write below.

13) Explain how you know.

##### 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.

14) Could this scatter plot represent those 20 bags and their absolute errors?

True or false? Write below.

##### Problem 3

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

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

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

##### Problem 4

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

Sketch a possible graph for this function given that:

﻿$D(3) = 4 \quad \quad \quad D(10) = 0 \quad \quad \quad D(5) > D(3)$﻿

##### Problem 5

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

18) What was the average rate of change during this time interval?

Show Work

19) What does the average rate of change tell us about the population growth?

##### Problem 6

Here is the graph of a function.

20) Which time interval shows the largest rate of change?

a)

From 0 to 2 seconds

b)

From 0 to 3 seconds

c)

From 4 to 5 seconds

d)

From 6 to 8 seconds

##### Problem 7

Here is the graph of ﻿$L(x)$﻿.

21) What is the value of ﻿$L(0)$﻿?

22) What is the value of ﻿$L(2)$﻿?

23) For what ﻿$x$﻿-values is ﻿$L(x) = 7$﻿?

Here is the graph of ﻿$R(x)$﻿.

24) What is the value of ﻿$R(0)$﻿?

25) What is the value of ﻿$R(2)$﻿?

26) For what ﻿$x$﻿-values is ﻿$R(x) = 7$﻿?

##### Problem 8

27) Select ﻿$\textbf{all}$﻿ systems that are equivalent to this system of equations: ﻿$\begin{cases} 4x + 5y = 1 \\ x - y = \frac{3}{8} \end{cases}$﻿

Write each corresponding letter in the answer box and separate letters with commas.

a) ﻿$\begin{cases} 4x + 5y = 1 \\ 4x - 4y = \frac{3}{2} \end{cases} \quad\quad$﻿ b) ﻿$\begin{cases} x + \frac{5}{4}y = \frac{1}{4} \\ x - y = \frac{3}{8} \end{cases} \quad\quad$﻿ c) ﻿$\begin{cases} 4x + 5y = 1 \\ 5x - 5y = 3 \end{cases} \quad\quad$﻿ d) ﻿$\begin{cases} 8x + 10y = 2 \\ 8x - 8y = 3 \end{cases} \quad\quad$﻿ e) ﻿$\begin{cases} x + y = \frac{1}{5} \\ x - y = \frac{3}{8} \end{cases}$﻿