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:
[tex]y=3cos(x-\pi)-4[/tex]
[tex]3 cos((x - \pi ) - 4 = 3 cos(x) - 4[/tex] because [tex]cos(x-\pi) = cos(x)[/tex]
[tex]-1 \leq cos(x) \leq 1[/tex]
[tex]-3 \leq 3cos(x) \leq 3[/tex]
[tex]-3-4 \leq 3 cos(x)-4 \leq 3-4[/tex]
[tex]-7 \leq 3 cos(x)\leq-1[/tex]
The range is -7 to -1 so the midpoint is [tex]\frac{-7-1}{2} =-4[/tex]
Therefore, the equation of the mid-line for the given function is y = -4.
