How does changing the function from f(x) = −5 cos 2x to g(x) = −5 cos 2x − 3 affect the range of the function? the function shifts down 3 units, so the range changes from −1 to 1 in f(x) to −4 to −2 in g(x). the function shifts down 3 units, so the range changes from −5 to 5 in f(x) to −8 to 2 in g(x). the function shifts down 5 units, so the range changes from −1 to 1 in f(x) to −6 to −4 in g(x). the function shifts down 5 units, so the range changes from −5 to 5 in f(x) to −10 to 0 in g(x).

The correct option is 2.

Step-by-step explanation:

The general form of a cosine function is

Where, a is amplitude, is period, C is phase shift and D is midline or vertical shift.

The given functions are

In f(x), D=0, it means midline is y=0. In g(x), D=-3, it means midline is y=-3. The graph of function f(x) shifts 3 units down to get the graph of g(x).

We know the the range of cosine function is [-1,1].

Multiply both the sides by -5. If we multiply or divide the inequality, then the sides of inequality is changed.

             .... (1)

The range of f(x) is [-5,5].

Subtract 3 from each side of inequality (1).

The range of g(x) is [-8,2].

The function shifts down 3 units, so the range changes from −5 to 5 in f(x) to −8 to 2 in g(x).

Therefore option 2 is correct.

attachment?

step-by-step explanation: