83144
AssignmentMultiple Select

Reflections and Dilations of Absolute Value Functions

Question 83144 • FL-1200310-Algebra 1 A

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.

Answer
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.

Explanation

The parent function y = |x| and f(x) = −|x| − 2 are both defined for every real x, so they have the same domain. The negative sign reflects the graph downward, and subtracting 2 shifts it down; the highest value is −2 at x = 0. Thus the range is all real numbers less than or equal to −2, so the true statements are that they share a domain and that the range is at most −2.

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