Question

How does changing the function from f(x) = −4 cos 3x to g(x) = −4 cos 3x − 6 affect the range of the function?

The function shifts down 4 units, so the range changes from −4 to 4 in f(x) to −8 to 0 in g(x).

The function shifts down 4 units, so the range changes from −1 to 1 in f(x) to −5 to −3 in g(x).

The function shifts down 6 units, so the range changes from −4 to 4 in f(x) to −10 to −2 in g(x).

The function shifts down 6 units, so the range changes from −1 to 1 in f(x) to −7 to −5 in g(x).

Answer 1

The function shifts down 6 units so the range will change from (-4, 4) to (-10,-2)
Option # 3

Answer 2

The function shifts down 6 units, so the range changes from −4 to 4 in f(x) to −10 to −2 in g(x).

Explanation:

Given : f(x) = −4 cos 3x and g(x) = −4 cos 3x − 6.

To find : How does changing the function affect the range of the function?

Solution : We have given that

Function change from f(x) = −4 cos 3x to g(x) = −4 cos 3x − 6.

By the transformation rule : f(x) →→→f(x) -k it mean function shifted down k unit .

Then Function would shift down 6 unit .

For f(x) = −4 cos 3x

Range: [ -4,4]

For g(x) = −4 cos 3x − 6.

Range : [-10 ,-2]

Therefore, The function shifts down 6 units, so the range changes from −4 to 4 in f(x) to −10 to −2 in g(x).