Find the period , range , and amplitude of the cosine function . y = - 4cos 8x )
The period of a cosine function is given by the formula T = 2π / b, where b is the coefficient of x inside the cosine function. In this case, b = 8, so the period is T = 2π / 8 = π/4.
The range of a cosine function is the set of all possible y-values it can take. Since the cosine function oscillates between -1 and 1, the range of this function is -4 to 4, because the amplitude is multiplied by the entire cosine function.
The amplitude of a cosine function is the absolute value of the coefficient in front of the cosine function. In this case, the amplitude is |-4| = 4.
Therefore, the period is π/4, the range is -4 to 4, and the amplitude is 4.