Determining the Dondailn and Range of an AbSolute Value Function 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 . Thes from the domain of the parent function that are also in the domain of this function.

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 open in the same direction.** - **Parent Function:** \( f(x) = |x| \) (opens upwards). - **Given Function:** \( f(x) = -|x| - 2 \) (opens downwards due to the negative sign). **Conclusion:** **False** ### 2. **The parent function and this function have the same range.** - **Parent Function Range:** \( y \geq 0 \). - **Given Function Range:** \( y \leq -2 \). **Conclusion:** **False** ### 3. **The parent function and this function have the same domain.** - **Parent Function Domain:** All real numbers (\( \mathbb{R} \)). - **Given Function Domain:** All real numbers (\( \mathbb{R} \)). **Conclusion:** **True** ### 4. **The range of the function is all real numbers less than or equal to -2.** - **Given Function:** \( f(x) = -|x| - 2 \). - When \( x = 0 \), \( f(0) = -0 - 2 = -2 \). - As \( |x| \) increases, \( f(x) \) decreases without bound. **Conclusion:** **True** ### 5. **The domain of the function is all real numbers greater than or equal to -2.** - **Given Function Domain:** All real numbers (\( \mathbb{R} \)). - The statement incorrectly describes the **range**, not the **domain**. **Conclusion:** **False** ### 6. **Thes from the domain of the parent function that are also in the domain of this function.** - This statement seems to be incomplete or unclear. If it implies that the domains overlap, it's redundant since both domains are the same. **Conclusion:** **Unclear/False** --- ### **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.** **Final Answer:** - 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.