Absolute Value Functions (Part 1)

ID: marob-sohus
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Created by Illustrative MathematicsIllustrative Mathematics, CC BY 4.0
Subject: Algebra, Algebra 2
Grade: 8-9
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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:

guess215108121920579absolute guessing error\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.

guess215108121920579absolute guessing errorABCDEFGHIJ\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.

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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.

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

True or false? Write below.

15) Explain your reasoning.

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.

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Problem 4

17) Function DD gives the height of a drone tt seconds after it lifts off.

Sketch a possible graph for this function given that:

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

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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?

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

Problem 6

Here is the graph of a function.

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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)L(x).

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21) What is the value of L(0)L(0)?

22) What is the value of L(2)L(2)?

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

Here is the graph of R(x)R(x).

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24) What is the value of R(0)R(0)?

25) What is the value of R(2)R(2)?

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

Problem 8

27) Select all\textbf{all} systems that are equivalent to this system of equations: {4x+5y=1xy=38\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) {4x+5y=14x4y=32\begin{cases} 4x + 5y = 1 \\ 4x - 4y = \frac{3}{2} \end{cases} \quad\quad b) {x+54y=14xy=38\begin{cases} x + \frac{5}{4}y = \frac{1}{4} \\ x - y = \frac{3}{8} \end{cases} \quad\quad c) {4x+5y=15x5y=3\begin{cases} 4x + 5y = 1 \\ 5x - 5y = 3 \end{cases} \quad\quad d) {8x+10y=28x8y=3\begin{cases} 8x + 10y = 2 \\ 8x - 8y = 3 \end{cases} \quad\quad e) {x+y=15xy=38\begin{cases} x + y = \frac{1}{5} \\ x - y = \frac{3}{8} \end{cases}