Question

identify the maximum and minimum values of the function y = 3 cos x in the interval [-2π, 2π]. Use your understanding of transformations, not your graphing calculator.

Answer 1

Do you know the min and max values of just cos x on that interval?

Answer 2

no

Answer 3

i am just completely lost on this one

Answer 4

the largest cosine can be is 1
and the smallest it can be is -1

Answer 5

and so what is the largest 3cos(x) can be?

Answer 6

3 ?

Answer 7

no my answer will be 3 and -3 ?

Answer 8

The minimum of f(x) = cos(x) is when x = pi + k*2pi where k is an integer, and this minimum is -1, and the maximum of f(x) = cos(x) is when x = k*2pi, and this maximum is +1. Multiply f(x) by 3 and you get a new function g(x) = 3*cos(x), so the minimum and maximum values of g(x) are now 3*-1 and 3*1, respectively.

Answer 9

oh ok i think i understand

Answer 10

Yey!

Answer 11

thank you :)