For the function y = - 1+6 cos (2π/7 (x-5)), what is the maximum value

5

Step-by-step explanation:

I'm assuming you want to find the maximum value of y

recall that for any cosine function y = A cos (g (x)), where g (x) is any arbitrary function, that A represents the amplitude of the cosine function.

By definition, the amplitude is the maximum the value which the cosine term can take.

hence for your expression:

y = - 1 + 6 cos (2π/7 (x-5))

max value of y = - 1 + (max value of cosine function)

max value of y = - 1 + (amplitude of cosine function)

max value of y = - 1 + 6 = 5