AnswersAlgebra III ALinear Piecewise Defined Functions

Absolute Value Functions and Translations Answers

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Which compound inequality is equivalent to for all real numbers a, b, and c, where ?

Question illustration
A
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Option A
B
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Option B
C
or
Option C
D
or
Option D
2
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Contessa is solving an absolute value inequality. She writes the compound inequality as her first step. Which inequality is Contessa solving?

Question illustration
A
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Option A
B
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Option B
C
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Option C
D
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Option D
3

A cyclist rides at an average speed of 31 miles per hour. The cyclist’s speed, s, can differ from the average by as much as 8 miles per hour. The absolute value inequality represents this situation. If the compound inequality and also represents this situation, what is the value of x in the compound inequality?

Question illustration
A
–8
B
–8 or 8
C
8
D
8 and –8
4

Which inequality is equivalent to ?

Question illustration
A
–9 > x – 4 < 9
B
–9 < x – 4 < 9
C
x – 4 < –9 or x – 4 < 9
D
x – 4 > –9 or x – 4 < 9
5

A student showed the steps below while solving the inequality by graphing.Step 1:Write a system of equations: Step 2: Graph the two equations:Step 3:Identify the values of x for which :x = 3 or x = 5Step 4:Write the solution in interval notation:What is the first step in which the student made an error?

Question illustration
A
Step 1, because the student should have written a compound statement with “and”
B
Step 2, because the student should have graphed the inequalities
Option B
C
Step 3, because the values for x for which also include values between 3 and 5
Option C
D
Step 4, because the solution is one continuous interval

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