Find the period, range, and amplitude of the cosine function. y=-4cos8x
The general form of a cosine function is y = A cos(Bx - C) + D, where A is the amplitude, B is the frequency (related to the period), C is the phase shift, and D is the vertical shift.
In this case, the given function is y = -4cos(8x).
Amplitude:
The amplitude of the function is the absolute value of the coefficient of the cosine function, which is |-4| = 4.
Period:
The period of a cosine function is given by 2π/B, where B is the coefficient of x inside the parentheses. In this case, B = 8, so the period is 2π/8 = π/4.
Range:
The range of the cosine function y = -4cos(8x) is from -4 to 4, since the amplitude is 4 and there is a negative sign in front of the cosine function.
Therefore, the amplitude is 4, the period is π/4, and the range is from -4 to 4.