Question

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

Answer 1

Answer:

The correct answer option is y = -4.

Step-by-step 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 $\frac{-7-1}{2} =-4$

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