What is the amplitude, period, and midline of f(x) = 3 cos(4x - π) + 2?

Solution:

Given, the function is f(x) = 3 cos(4x - π) + 2 --- (1)

We have to find the amplitude, period and midline of the function.

The standard form of a cosine function is

g(x) = a cos(bx + c) + d --- (2)

Where, a is amplitude

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

d is midline

Comparing (1) and (2)

a = 3

b = 4

d = 2

Amplitude of the function is a = 3

The period of the function is

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

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

Midline of the function is d = 2

Therefore, the amplitude, period and midline of the function are 3, \(\frac{\pi }{2}\) and 2.

What is the amplitude, period, and midline of f(x) = 3 cos(4x - π) + 2?

Summary:

The amplitude, period, and midline of f(x) = 3 cos(4x - π) + 2 are 3, \(\frac{\pi }{2}\) and 2.