Question

How does changing the function from f(x) = -5 cos 2x to g(x) = -5 cos 2x-3 affect the range of the function?

Answer 1

Each element in the range of g(x) is 3 less than the corresponding element in the range of f(x).

Answer 2

See below.

In short, by having vertical shift will affect range from -1 ≤ y ≤ 1 to -1 + a ≤ y ≤ 1 + a

Explanation:

Generally, a cosine function without vertical shift will always have range equal to -1 ≤ y ≤ 1

If there is given vertical shift, our range will change to -1 + a ≤ y ≤ 1 + a

An example is if we are given the function of cos(x), this always has range of -1 ≤ y ≤ 1 because there is no vertical shift.

But if we have cos(x) + 1, we have vertical shift which is 1. Then the range will be -1+1 ≤ y ≤ 1+1 which equals to 0 ≤ y ≤ 2.

Hence, the function of -5cos(2x) has only range of -1 ≤ y ≤ 1 but the function of -5cos(2x) - 3 will have range of -1-3 ≤ y ≤ 1-3 which equals to -4 ≤ y ≤ -2