The graph of a trigonometric function oscillates between y=1 and y=-7. It reaches its maximum at x= pi and its minimum at x=3pi. which of the following could be the equation of the function?

A) f(x)=4 cos x/2-3
B) f(x)=4 sin x/2-3
C) f(x)=4 sin 2x-3
D) f(x)=8 sin x/2-3

I think it’s D but I’ve been told it was and wasnt that answer :/ help pls!

isn't

try B

To determine which equation could represent the given graph, we need to analyze the given information about the oscillations, maxima, and minima.

First, we are told that the graph oscillates between y = 1 and y = -7. This implies that the amplitude of the function is 6, calculated by the absolute difference between the maximum and minimum values of y:

Amplitude = |Maximum value of y - Minimum value of y| = |1 - (-7)| = 6.

Next, we are informed that the maximum value of the function is reached at x = π and the minimum value at x = 3π. We know that the period of a trigonometric function is the distance between two consecutive peaks or troughs. In this case, the distance between the maximum and minimum is 2π, which corresponds to one period of the function:

Period = 2π.

Now, let's analyze each answer choice:

A) f(x) = 4 cos(x/2) - 3
B) f(x) = 4 sin(x/2) - 3
C) f(x) = 4 sin(2x) - 3
D) f(x) = 8 sin(x/2) - 3

Considering the amplitude, the only choices that have an amplitude of 6 (matching the given information) are options B and D. Now we need to check if either of these options satisfies the condition of the maximum occurring at x = π.

In option B, f(x) = 4 sin(x/2) - 3, the maximum of the graph would occur when sin(x/2) = 1, which happens at x = 2πk, where k is an integer. This means that the maximum would not occur at x = π.

On the other hand, in option D, f(x) = 8 sin(x/2) - 3, the maximum of the graph would occur when sin(x/2) = 1/2, which happens at x = π + 2πk, where k is an integer. This satisfies the condition of the maximum occurring at x = π when k = 0.

Therefore, the equation that could represent the given graph is:

D) f(x) = 8 sin(x/2) - 3.

Make sure to double-check the question and its requirements to ensure the correct answer!