Which satements are tue abour the function $$ f(x)=-|x|-2 $$ ? Check all that apply. - The parent function and this function and this function haven in, the same 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.

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Let's analyze each statement regarding the function $$ f(x) = -|x| - 2 $$ and determine which ones are true.

1. **The parent function and this function have the same range.**
   
   - **False.** 
     - **Parent Function ($$ g(x) = |x| $$):** 
       - **Domain:** All real numbers ($$ \mathbb{R} $$).
       - **Range:** $$ y \geq 0 $$.
     - **Given Function ($$ f(x) = -|x| - 2 $$):**
       - **Domain:** All real numbers ($$ \mathbb{R} $$).
       - **Range:** $$ y \leq -2 $$.
     - **Conclusion:** The ranges are different.

2. **The parent function and this function have the same domain.**
   
   - **True.**
     - Both the parent function $$ g(x) = |x| $$ and the given function $$ f(x) = -|x| - 2 $$ have a domain of all real numbers ($$ \mathbb{R} $$).

3. **The range of the function is all real numbers less than or equal to -2.**
   
   - **True.**
     - For $$ f(x) = -|x| - 2 $$:
       - The smallest value of $$ |x| $$ is 0 (when $$ x = 0 $$).
       - $$ f(0) = -0 - 2 = -2 $$.
       - As $$ |x| $$ increases, $$ f(x) $$ decreases, making the range $$ y \leq -2 $$.

4. **The domain of the function is all real numbers greater than or equal to -2.**
   
   - **False.**
     - The domain of $$ f(x) = -|x| - 2 $$ is all real numbers ($$ \mathbb{R} $$), not restricted to numbers greater than or equal to -2.

5. **There are no values from the domain of the parent function that are also in the domain of this function.**
   
   - **False.**
     - Both the parent function and $$ f(x) $$ share the same domain of all real numbers ($$ \mathbb{R} $$).

**Summary of True Statements:**
- 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.

Answer: All except statements 2 and 3 are false. The true statements are statements 2 and 3.
The true statements are: - 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.

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