Reflections and Dilations of Absolute Value Functions

Question 1

Which describes how the parent function, f(x) = |x|, is transformed to show the function f(x) = 0.1|x – 3|?

Revolt · Accepted Answer

B: It is wider and shifted 3 units to the right.

Question 2

Which absolute value functions will be narrower than the parent function, f(x) = |x|? Check all that apply.f(x) = |x|f(x) = |x – 2|f(x) = |x| + 3f(x) = 2.9|x|f(x) = 1.2|x + 8|f(x) = 0.7|x| – 3.2

Revolt · Accepted Answer

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Question 3

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

Revolt · Accepted Answer

C:

Question 4

Which is the equation of the function?f(x) = 3|x| + 1f(x) = 3|x – 1|f(x) = |x| + 1f(x) = |x – 1|

Revolt · Accepted Answer

A: f(x) = 3|x| + 1

Question 5

✔ all real numbersall numbers greater than or equal to 2all numbers less than or equal to 2

Revolt · Accepted Answer

A: ✔ all real numbers

Question 6

Which function is represented by the graph?|–x + 3|–|x + 3|–|x| + 3|–x| + 3

Revolt · Accepted Answer

C: –|x| + 3

Question 7

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?

Revolt · Accepted Answer

B: (–3, 7.5)

Question 8

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.

Revolt · Accepted Answer

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.

Question 9

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.

Revolt · Accepted 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.

Question 10

all real numbersall numbers greater than or equal to 2✔ all numbers less than or equal to 2

Revolt · Accepted Answer

C: ✔ all numbers less than or equal to 2

Reflections and Dilations of Absolute Value Functions Answers

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