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
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20 questions

Absolute Value Functions (Part 2)

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Problem 1

The absolute value function can be defined using piecewise notation.

A(x)={x,x0x,x<0A(x) = \begin{cases} x, & x \geq 0 \\ -x, & x < 0 \end{cases}

Use this notation to find the following values:

1) A(10)A(10)

2) A(0)A(0)

3) A(3)A(-3)

4) A(3.14159)A(3.14159)

5) A(x)=7A(x) = 7

6) A(x)=5A(x) = -5

Problem 2

Here are four equations of absolute value functions and three coordinate pairs. Each coordinate pair represents the vertex of the graph of an absolute value function.

a) (-9, 0) \quad\quad\quad b) (9, 0) \quad\quad\quad c) (0, -9)

Match the equation of each function with the coordinates of the vertex of its graph, writing the letter of the coordinate pair in the answer box. The vertex coordinates of the graph of one equation are not shown. Write "No match" in that answer box.

7) p(x)=x9p(x) = |x - 9|

8) q(x)=x+9q(x) = |x| + 9

9) r(x)=x+9r(x) = |x + 9|

10) t(x)=x9t(x) = |x| - 9

Problem 3

11) Function GG is defined by the equation G(x)=xG(x) = |x|.

Function RR is defined by the equation R(x)=x+2R(x) = |x| + 2.

Describe how the graph of function RR relates to the graph of GG, or sketch the graphs of the two functions to show their relationship.

Problem 4

12) Here is the graph of a function.

Select the equation for the function represented by the graph.

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a)

yy=x|x|-5

b)

yy=x|x|+5

c)

yy=x|x-5|

d)

yy=x|x+5|

Problem 5

The temperature was recorded at several times during the day. Function TT gives the temperature in degrees Fahrenheit, nn hours since midnight.

Here is a graph for this function.

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13) Pick two consecutive points and connect them with a line segment.

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14) Estimate the slope of that line.

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15) Explain what that estimated value means in this situation.

16) Pick two non-consecutive points and connect them with a line segment.

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17) Estimate the slope of that line.

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18) Explain what that estimated value means in this situation.

Problem 6

19) A tennis ball is dropped from an initial height of 30 feet. It bounces 5 times, with each bounce height being about 23\frac{2}{3} of the height of the previous bounce.

Sketch a graph that models the height of the ball over time. Be sure to label the axes.

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Problem 7

20) Here are two graphs representing functions ff and gg.

Identify at least two values of xx at which the inequality g(x)>f(x)g(x) > f(x) is true.

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