Question

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

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.

Answer 1

Functions are represented by equations and graphs

The true statements about the function f(x) = -|x| - 2 are:

• 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.

How to determine the true statements

The function is given as:

$f(x) = -|x| - 2$

The above function is an absolute value function, reflected over the y-axis and then shifted down by 2 units from its parent function

The parent function of an absolute value function is:

$y =|x|$

Given that the function f(x) is reflected, then it means that it does not have the same range as the parent function, and they do not face the same direction.

Hence, the true statements are (c) and (d)

Read more about function transformation at:

https://brainly.com/question/1548871