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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) -2.5< x<-1


A

(Choice B) 0< x < 1


B

(Choice C) 2.5< x< 3.5


C

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

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1 answer

To determine where the function \( h(x) \) is decreasing based on the description of the graph provided, let's summarize the behavior of the graph at different intervals:

  1. From \( x = -4 \) to \( x = -3.5 \): The function is decreasing towards the x-intercept at \( x = -3.5 \).
  2. From \( x = -3.5 \) to \( x = -2.5 \): The function reaches a local minimum at \( (-2.5, 10) \), indicating it is still decreasing in this interval.
  3. From \( x = -2.5 \) to \( x = -1 \): The function starts increasing after reaching the local minimum at \( x = -2.5\).
  4. From \( x = 0 \) to \( x = 1 \): The function is increasing leading up to the local maximum at \( x = 1.5\), so this interval is not decreasing.
  5. From \( x = 1.5 \) to \( x = 3.5 \): The function decreases after the local maximum at \( x = 1.5\) until it reaches the next x-intercept at \( x = 3.5\).

To evaluate the choices provided:

  • (Choice A) \( -2.5 < x < -1 \): This is incorrect because the function is increasing here (from \( x = -2.5 \) to \( x = -1 \)).

  • (Choice B) \( 0 < x < 1 \): Incorrect; the function is increasing on this interval.

  • (Choice C) \( 2.5 < x < 3.5 \): Correct; the function is decreasing in this interval from the local maximum at \( x = 1.5 \) until the next intercept at \( x = 3.5 \).

  • (Choice D) None of the above: Incorrect; since Choice C is valid.

Thus, the correct answer is:

(Choice C) \( 2.5 < x < 3.5 \).