Find the domain, period, range, and amplitude of the cosine function. y = -6cos4x

Solution:

Given, the function is y = -6cos(4x) --- (1)

We have to find the domain, period, range and amplitude of the cosine function.

The standard form of a cosine function is

g(x) = a cos(bx + c) + d  --- (2)

Where, a is amplitude

Period is \(\frac{2\pi }{b}\)

C is the phase shift and

d is midline or the vertical shift

Comparing (1) and (2),

a = -6

bx = 4x

b = 4

c = 0, d = 0

Amplitude of the function is a = -6

The period of the function is

\(\frac{2\pi }{4}\) = \(\frac{\pi }{2}\)

Period = π/2

Domain is all real numbers because there is a y value for every x.

The range of the function lies between the positive and negative amplitude.

Range = -6 ≤ y ≤ 6

Therefore, the domain is all real numbers, range is -6 ≤ y ≤ 6, amplitude is -6 and period is π/2.

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Find the domain, period, range, and amplitude of the cosine function. y = -6cos4x

Summary:

The cosine function y = -6cos4x has domain = all real numbers, range = -6 ≤ y ≤ 6, amplitude = -6, period = π/2.