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

Solution:

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

b = 2

d = 3

Amplitude of the function is a = 4

The period of the function is

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

Period = π

Midline of the function is d = 3

Therefore, the amplitude, period and midline of the function are 4 ,π and 3.

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

Summary:

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