Question

What is the equation of the midline for the function y = 3cos(x - π ) - 4?

y = -4
y = -π
y = 4
y = π

Answer 1

The correct answer option is y = -4.

Explanation:

We are to find the equation of the mid-line for the following function:

`y=3cos(x-\pi)-4`

`3 cos((x - \pi ) - 4 = 3 cos(x) - 4` because
`cos(x-\pi) = cos(x)`

`-1 \leq cos(x) \leq 1`

`-3 \leq 3cos(x) \leq 3`

`-3-4 \leq 3 cos(x)-4 \leq 3-4`

`-7 \leq 3 cos(x)\leq-1`

The range is -7 to -1 so the midpoint is
`(-7-1)/(2) =-4`

Therefore, the equation of the mid-line for the given function is y = -4.