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!
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)
8g+t
To determine the correct equation for the trigonometric function, we need to consider the given information about its behavior and the maximum and minimum points.
The general form of a trigonometric function that oscillates between an amplitude of "A" and a midpoint of "B" is:
f(x) = A sin(kx) + B,
where "A" is the amplitude, "B" is the midpoint, and "k" determines the period of the function.
In this case, the function oscillates between y = 1 and y = -7, so the amplitude is half the difference between these two values:
Amplitude = (1 - (-7))/2 = 8/2 = 4.
The midpoint is the average of the maximum and minimum values:
Midpoint = (1 + (-7))/2 = -6/2 = -3.
Now, let's analyze the given options to find the correct equation of the function.
A) f(x) = 4 cos(x/2) - 3.
This equation is in the cosine function form, and we need a sine function because the provided equation oscillates between y = 1 and y = -7. So option A is incorrect.
B) f(x) = 4 sin(x/2) - 3.
This equation is in the sine function form and matches the requirements of our problem. The amplitude is 4, and the midpoint is -3. Therefore, option B could be the correct equation.
C) f(x) = 4 sin(2x) - 3.
This equation has a period of π/2, which is shorter than the given information of the function oscillating between x = π and x = 3π. Therefore, option C is incorrect.
D) f(x) = 8 sin(x/2) - 3.
This equation has an amplitude of 8, which is twice the amplitude we calculated from the given information. Therefore, option D is incorrect.
Based on our analysis, the correct equation for the given function is:
f(x) = 4 sin(x/2) - 3.
So, the correct answer is option B.
To determine the equation of the trigonometric function, we can analyze the given information and compare it with the general forms of the cosine and sine functions.
We are told that the graph oscillates between y = 1 and y = -7, which means the amplitude is 6 (the difference between the maximum and minimum values). This means that the coefficient of either the cosine or sine function must be 6.
The function reaches its maximum at x = pi, which corresponds to the maximum value of the cosine or sine function. At this point, the cosine function has a value of 1, while the sine function has a value of 0. Similarly, the function reaches its minimum at x = 3pi, where the cosine function has a value of -1, and the sine function has a value of -1.
Let's go through the options and see which one satisfies the given conditions:
A) f(x) = 4cos(x/2) - 3:
The maximum value of this function occurs at x = 2pi, not pi, so this option doesn't match the given conditions.
B) f(x) = 4sin(x/2) - 3:
The maximum value of this function occurs at x = pi, which matches the given condition. The amplitude is also 4 * 6 = 24, which is inconsistent.
C) f(x) = 4sin(2x) - 3:
The maximum value of this function occurs at x = pi/2, not pi, so this option doesn't match the given conditions.
D) f(x) = 8sin(x/2) - 3:
The maximum value of this function occurs at x = pi, which matches the given conditions. The amplitude is 8 * 6 = 48, which is consistent.
Based on the given information, option D is the most suitable equation for the given conditions.