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Question 1
Select the correct response.(1 point)
The graph of the function y=−2(x+4)−−−−−−√3
is
increasing
.

1 answer

To determine whether the function \( y = -2\sqrt{x+4} - 3 \) is increasing or decreasing, we need to analyze the components of the function.

The function contains a square root, which is defined for \( x + 4 \geq 0 \) (or \( x \geq -4 \)). The square root function is non-negative, and since it is multiplied by -2, the entire term \(-2\sqrt{x+4}\) will be non-positive and will decrease as \( x \) increases.

Thus, the function \( y = -2\sqrt{x+4} - 3 \) is a decreasing function. Therefore, the correct response is that the graph of the function is not increasing; it is decreasing.

The correct response should be:

  • Decreasing.