11 12 13 14 15 TIME REMAMUNV 01:06:29 Which of the following describes the graph of $$ y=\sqrt{-4 x-36} $$ compared to the parent square root function? stretched by a factor of 2 , reflected over the $$ x $$-axis, and translated 9 units right stretched by a factor of 2 , reflected over the $$ x $$-axis, and translated 9 units left stretched by a factor of 2 , reflected over the $$ y $$-axis, and translated 9 units right stretched by a factor of 2 , reflected over the $$ y $$-axis, and translated 9 units left

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UpStudy AI · Accepted Answer

To analyze the transformations of the graph $$ y = \sqrt{-4x - 36} $$ compared to the parent square root function $$ y = \sqrt{x} $$, let's break down the equation step by step.

1. **Factor Inside the Square Root:**
   $$
   y = \sqrt{-4x - 36} = \sqrt{-4(x + 9)}
   $$
   
2. **Separate Constants and Variables:**
   $$
   y = \sqrt{-4} \cdot \sqrt{x + 9} = 2\sqrt{-(x + 9)}
   $$
   
3. **Identify Transformations:**
   - **Reflection:** The negative sign inside the square root ($$ -x $$) indicates a reflection over the **$$ y $$-axis**.
   - **Horizontal Shift:** The term $$ (x + 9) $$ implies a shift **9 units to the left**.
   - **Vertical Stretch:** The coefficient $$ 2 $$ outside the square root stretches the graph **vertically by a factor of 2**.

4. **Summary of Transformations:**
   - **Stretched vertically by a factor of 2**
   - **Reflected over the $$ y $$-axis**
   - **Translated 9 units to the left**

**Therefore, the correct description of the graph is:**

**Stretched by a factor of 2, reflected over the y-axis, and translated 9 units left.**
The graph is stretched vertically by a factor of 2, reflected over the y-axis, and translated 9 units to the left.

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