f ( x ) = − 2 cos ( 4 π x )

Question

Find the following:

Period

Maximum

Minimum

Equation of the midline

Answer 1

Hello Mallory!

Note that this is a periodic function, because cosine is a periodic function, with period of 2π. Therefore, to find the period, we just have to find the period, we just have to divide 2π/4π, which is 1/2.

To find the maximum and minimum, we just have to remember that the function cosine has the maximum of 1 and the minimum of -1. However, there is a catch, because of the minus sign in this function, its maximum is when the cosine is in its minimum and vice-versa.

The maximum of the function is -2*(-1) = 2 and the minimum is -2*(1) = - 2

The equation of the midline is the average of the maximum and minumum, which is the x-axis, with equation x = 0