Select the correct response. The graph of the function y=−2(x+4)−−−−−−√3 is increasing/decreasing explain your answer

Question

Select the correct response.  The graph of the function y=−2(x+4)−−−−−−√3 is increasing/decreasing   explain your answer

GPT-4o mini · Answer

To analyze whether the function $ y = -2\sqrt{x + 4} - 3 $ is increasing or decreasing, we can examine the structure of the function. 1. **Function Form**: The function contains a square root, $ \sqrt{x + 4} $, which is a monotonically increasing function over its domain (where $ x + 4 \geq 0 $ or $ x \geq -4 $). 2. **Coefficient of $-2$**: The square root is multiplied by $-2$. This reflection across the x-axis indicates that the output of the function decreases as $ \sqrt{x + 4} $ increases. 3. **Vertical Shift**: The entire function is then shifted down by 3 units due to the $-3$ at the end. This does not affect the increasing or decreasing nature of the function. ### Conclusion: Since we have a negative coefficient in front of the square root, the function $ y = -2\sqrt{x + 4} - 3 $ is decreasing. As $ x $ increases (within its domain), $ y $ decreases. Thus, the graph of the function is **decreasing**. **Explanation**: Because the square root function is increasing and is multiplied by -2, it reverses the behavior to decreasing.