Absolute Value Functions (Part 2)

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Created by Illustrative MathematicsIllustrative Mathematics, CC BY 4.0
Subject: Algebra, Algebra 2
Grade: 8-9
Standards: HSF-BF.A.1.aHSF-IF.C.7.bHSF-IF.CHSF-BF.A.1HSF-BF.B.3
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22 questions

Absolute Value Functions (Part 2)

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Temperature in Toronto

Toronto is a city at the border of the United States and Canada, just north of Buffalo, New York. Here are twelve guesses of the average temperature of Toronto, in degrees Celsius, in February 2017.

5, 2, -5, 3, 0, -1, 1.5, 4, -2.5, 6, 4, -0.5

The actual average temperature of Toronto in February 2017 was 0 degree Celsius.

1) Use this information to sketch a scatter plot representing the guesses, xx, and the corresponding absolute guessing errors, yy.

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2) What rule can you write to find the output given the input?

The Distance Function

The function AA gives the distance of xx from 0 on the number line.

Complete the table. Write the values for the labeled cells in the answer boxes below.

xA(x)8AB5.6πC12DE10F12G1H5.6IJ8\begin{array}{|c|c|} \hline \\[-1em] x & A(x) \\[-1em] \\ \hline \\[-1em] 8 & \text{A} \\[-1em] \\ \hline \\[-1em] \text{B} & 5.6 \\[-1em] \\ \hline \\[-1em] \pi & \text{C} \\[-1em] \\ \hline \\[-1em] \frac{1}{2} & \text{D} \\[-1em] \\ \hline \\[-1em] \text{E} & 1 \\[-1em] \\ \hline \\[-1em] 0 & \text{F} \\[-1em] \\ \hline \\[-1em] -\frac{1}{2} & \text{G} \\[-1em] \\ \hline \\[-1em] -1 & \text{H} \\[-1em] \\ \hline \\[-1em] -5.6 & \text{I} \\[-1em] \\ \hline \\[-1em] \text{J} & 8 \\[-1em] \\ \hline \end{array}

3) Cell A

4) Cell B

5) Cell C

6) Cell D

7) Cell E

8) Cell F

9) Cell G

10) Cell H

11) Cell I

12) Cell J

13) Sketch a graph of function AA.

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Andre and Elena are trying to write a rule for this function.

\boldsymbol{\cdot} Andre writes: {x,x0x,x<0\begin{cases} x, & x \geq 0 \\ -x, & x < 0 \end{cases}

\boldsymbol{\cdot} Elena writes: A(x)=xA(x) = |x|

14) Explain why both equations correctly represent the function AA.

Moving Graphs Around

Graph the functions f(x)=x+af(x) = |x + a| and g(x)=x+bg(x) = |x| + b. Experiment with different values of aa and bb and observe what happens to the graphs.

15) How does changing aa change the graph?

16) How does changing bb change the graph?

More Moving Graphs Around

Here are five equations and four graphs.

Equation 1: y=x3y = |x - 3| \quad \quad Equation 2: y=x9+3y = |x - 9| + 3 \quad \quad Equation 3: y=x6y = |x| - 6\quad \quad Equation 4: y=x+3y = |x + 3| \quad \quad Equation 5: y=x+36y = |x + 3| - 6

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Match each equation with a graph that represents it. Write the letter of the graph that corresponds to each equation. One equation has no match. (Write "No match" for this equation.)

17) Equation 1

18) Equation 2

19) Equation 3

20) Equation 4

21) Equation 5

22) For the equation without a match, sketch a graph on the blank coordinate plane.

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