Question

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

Answer 1

The difference between f(x) and g(x) is the +5 . Adding 5 to the end will increase all y-values obtained for the function. The range is all possible y-values of the function. The function is a wave, which moves between high and low points; +5 in the positive y direction and -5 in the negative y direction is increasing the range by 10.

Answer 2

Change in function f(x) to g(x): 5 unit up

Range: [2,8]

Explanation:

Given:

`f(x)=3\sin2x`

`g(x)=3\sin(2x)+5`

First we have to see the change from f(x) to g(x).

`g(x)=3\sin(2x)+5`

`g(x)=f(x)+5`

`f(x)=3\sin2x`

If we shift f(x) 5 unit up to get g(x)

`g(x)=3\sin(2x)+5`

Effect: f(x) shift 5 unit up

Now we see change in range.

Range of
`f(x)=3\sin2x`

`[-3,3]`

Graph shift 5 unit up.

So, Range will shift 5 unit up.

Range of
`g(x)=3\sin(2x)+5`

`[-3+5,3+5]\Rightarrow [2,8]`

Hence, The range of g(x) is [2,6]