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AssignmentMultiple Select

Absolute Value Functions and Translations

Question 7 • FL-1200310-Algebra 1 A

Which statements are true about the function f(x) = –|x| – 2? Check all that apply.

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; statement C is true. The negative sign reflects the graph downward, and subtracting 2 shifts it down, making its highest value –2 at x = 0. Thus its range is all real numbers less than or equal to –2, so D is true. The functions open in opposite directions and do not have the same range.

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