
a.
Create a table of f(x) and g(x) values for x=−4 to x=4 .
a.

Answer to Problem 39PPS
xf(x)−40−3−1−2−2−1−30−41−32−23−140 , xg(x)−412−39−26−1300132639412
Explanation of Solution
Given information:
Consider the following absolute value functions.
f(x)=|x|−4
g(x)=|3x|
Create a table of f(x) and g(x) values for x=−4 to x=4 .
Calculation:
Consider the function
f(x)=|x|−4
Calculate the function values using TI83 calculator for x=−4 to x=4
Press Y= and enter the equation. To enter the absolute function press MATH and select NUM and then press 1 to select abs function
Press 2nd
GRAPH to see the tabular values
Scroll the table and to view the values for different
xf(x)−40−3−1−2−2−1−30−41−32−23−140
Consider the function
g(x)=|3x|
Calculate the function values using TI83 calculator for x=−4 to x=4
Press Y= and enter the equation. To enter the absolute function press MATH and select NUM and then press 1 to select abs function
Press 2nd
GRAPH to see the tabular values
Scroll the table and to view the values for different x
xg(x)−412−39−26−1300132639412
b.
Graph the functions on separate graphs.
b.

Answer to Problem 39PPS
Explanation of Solution
Given information:
Consider the following absolute value functions.
f(x)=|x|−4
g(x)=|3x|
Graph the functions on separate graphs.
Calculation:
Press GRAPH for plotting for the graph of the function f(x)=|x|−4
Press GRAPH for plotting for the graph of the function g(x)=|3x|
c.
Determine the slope between each two consecutive points in the table.
c.

Answer to Problem 39PPS
xf(x)slope−of−f(x)g(x)slope−of−g(x)−4012−3−1−19−3−2−2−16−3−1−3−13−30−4−10−31−31332−21633−1193401123
Explanation of Solution
Given information:
Consider the following absolute value functions.
f(x)=|x|−4
g(x)=|3x|
Determine the slope between each two consecutive points in the table.
Calculation:
Consider the slope of the line joining two points (x1y1),(x2y2) is m=y2−y1x2−x1
Hence, the slope between two consecutive points for f(x) and g(x)
xf(x)slope−of−f(x)g(x)slope−of−g(x)−4012−3−1−19−3−2−2−16−3−1−3−13−30−4−10−31−31332−21633−1193401123
d.
Describe how the slopes of the two sections of an absolute value graph are related.
d.

Answer to Problem 39PPS
The slope is constant for each sections of the graph.
Explanation of Solution
Given information:
Consider the following absolute value functions.
f(x)=|x|−4
g(x)=|3x|
Describe how the slopes of the two sections of an absolute value graph are related.
Calculation:
The two sections of an absolute value graph have opposite slopes.
Hence, the slope is constant for each sections of the graph.
Chapter 2 Solutions
Algebra 2
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