f ( x ) = − 2 cos ( 4 π x ) Find the following:

Question

Period

Maximum

Minimum

Equation is the midline

Answer 1

Let's examine the given cosine function

f(x) = (-2). Cos (4πx)

(-2) is the amplitude of the function

The cosine function has the period 2π, i.e. when

4πx = 2π, or x = 1/2

the function repeats itself. The period of this function is therefore, 1/2.

When cos(4πx) = -1, the function achieves the maximum value +2

When cos(4πx) = +1, the function achieves the minimum value -2