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?

Question

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!

Answer 1

max - min = 1 - (-7) = 8
so a = 4 , could be any of the first 3

from 3π to π = 2π , so the period is 4π
2π/k = 4π
4πk = 2π
k = 1/2
so we should see either sin(x/2) or cos(x/2)

so it has to be either a) or b)
test a)
if x = π ,
y = 4cos(π/2) - 3 = 4(0) - 3 = -3 ≠ 1 , that is incorrect

double check for b)
if x = π , y = 4sin(π/2) - 3 = 4(1) - 3 = 1 , yeah!!!! , it is b)

Answer 2

8g+t