Question

Select all the intervals where

is decreasing.
A coordinate plane. The x-axis scales by one, and the y-axis scales by four. The graph of y equals h of x is a continuous curve. From left to right, it passes through the point negative four, eight. It decreases though the x-intercept negative three and one-half, zero until the local minimum at negative two and one-half, ten. Then it increases through the x-intercept negative one, zero and the y-intercept zero, fourteen. It continues to increases until the local maximum at one and one-half, twenty-eight. Then it decreases though the point three, sixteen, the x-intercept three and one-half, zero, and the point four, negative sixteen. All values are estimates.

















Choose all answers that apply:
Choose all answers that apply:
(Choice A)


A

(Choice B)


B

(Choice C)


C

(Choice D) None of the above
D
None of the above

10 of 30

Answer 1

Based on the description of the graph of \( h(x) \), it is decreasing in the following intervals:

1. From the x-value where it begins to decrease (just after the point \((-4, 8)\)) to the x-intercept at \((-3.5, 0)\).
2. From the local maximum at \((-2.5, 10)\) to the x-intercept at \((-1, 0)\).
3. From the local maximum at \((1.5, 28)\) to the x-value where it intersects the x-axis at \((3.5, 0)\).
4. From the x-value where it intersects the x-axis at \((3.5, 0)\) to the point \((4, -16)\).

So the intervals for \( h(x) \) being decreasing would be:

- \((-4, -3.5)\)
- \((-2.5, -1)\)
- \((1.5, 3.5)\)
- \((3.5, 4)\)

Without specific numerical options A, B, or C provided for the decreasing intervals, I cannot match them directly to these intervals. If the choices correspond to the intervals I've identified, you would select those particular choices.

If you're asking if there's a "None of the Above" option (Choice D), you would choose that only if none of A, B, or C accurately reflect the decreasing intervals described above.