Find the period, range, and amplitude of the cosine function.
y = –4 cos 8x
A. period = 1/4, range = –4 ≤ y ≤ 4, amplitude = 4
B. period = 1/4pi, range = –4 ≤ y ≤ 4, amplitude = 4
C. period = 1/2pi, range = –4 ≤ y ≤ 4, amplitude = –4
D. period = 1/2, range = –4 ≤ y ≤ 4, amplitude = –4
A. period = 1/8pi (or 1/4), range = -4 ≤ y ≤ 4, amplitude = 4
To find the period, range, and amplitude of the cosine function y = –4 cos 8x, we can use the standard form of the cosine function:
y = A cos(Bx)
In this case, A is the amplitude and B determines the period.
The amplitude can be found by taking the absolute value of the coefficient in front of the cosine function. In this case, the amplitude is |(-4)| = 4. So the amplitude is 4.
The period can be found by dividing 2π by the coefficient in front of x. In this case, the period is 2π / 8 = π / 4.
So, the correct answer is:
A. period = π / 4, range = –4 ≤ y ≤ 4, amplitude = 4