AnswersFL-1200370-Algebra 1-A Semester 2Reflections and Dilations of Absolute Value Functions

Reflections and Dilations of Absolute Value Functions Answers

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1
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Which graph represents the function f(x) = 2|x|?

A
Option A
B
Option B
C
Option C
D
Option D
2
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What did you include in your response? Check all that apply.

A
Both Shawn and Brielle are correct.
B
The absolute value parent function is symmetric with respect to the y-axis.
C
The graphs of f(x) = 2|–x| and f(x) = 2|x| are identical because the absolute value of negative x is a reflection across the y-axis.
D
If you substitute the three given points into both functions, they produce true statements.
3

Which is the equation of the function?

A
f(x) = 3|x| + 1
Option A
B
f(x) = 3|x – 1|
Option B
C
f(x) = |x| + 1
Option C
D
f(x) = |x – 1|
Option D
4

Which function is represented by the graph?

A
|–x + 3|
B
–|x + 3|
C
–|x| + 3
D
|–x| + 3
5

The graph of f(x) = |x| has been stretched by a factor of 2.5. If no other transformations of the function have occurred, which point lies on the new graph?

Answer not available
6

Which statements are true about the function f(x) = –|x| – 2? Check all that apply.The parent function and this function open in the same direction.The parent function and this function have the same range.The parent function and this function have the same domain.The range of the function is all real numbers less than or equal to –2.The domain of the function is all real numbers greater than or equal to –2.There are no values from the domain of the parent function that are also in the domain of this function.

A
The parent function and this function open in the same direction.
B
The parent function and this function have the same range.
C
The parent function and this function have the same domain.
D
The range of the function is all real numbers less than or equal to –2.
E
The domain of the function is all real numbers greater than or equal to –2.
F
There are no values from the domain of the parent function that are also in the domain of this function.
7

The graph of an absolute value function contains the points (1, 2), (0, 0), and (–1, 2). Shawn thinks the function this graph represents is f(x) = 2|–x|. Brielle thinks the function this graph represents is f(x) = 2|x|. Determine who is correct and explain why.

Answer:

Both Shawn and Brielle are correct. The functions f(x) = 2|-x| and f(x) = 2|x| are equivalent because the absolute value of a number is the same as the absolute value of its opposite (|-x| = |x|). When you substitute the points (1, 2), (0, 0), and (–1, 2) into both equations, they yield true statements. Graphically, f(x) = 2|-x| represents a reflection of f(x) = 2|x| across the y-axis, and since the absolute value parent function is already symmetric with respect to the y-axis, the graphs are identical.

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