Respuesta :

Catya
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.
isyllus

Answer:

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

Range: [2,8]

Step-by-step explanation:

Given:

[tex]f(x)=3\sin2x[/tex]

[tex]g(x)=3\sin(2x)+5[/tex]

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

[tex]g(x)=3\sin(2x)+5[/tex]

[tex]g(x)=f(x)+5[/tex]

[tex]f(x)=3\sin2x[/tex]

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

[tex]g(x)=3\sin(2x)+5[/tex]

Effect: f(x) shift 5 unit up

Now we see change in range.

Range of [tex]f(x)=3\sin2x[/tex]

[tex][-3,3][/tex]

Graph shift 5 unit up.

So, Range will shift 5 unit up.

Range of [tex]g(x)=3\sin(2x)+5[/tex]

[tex][-3+5,3+5]\Rightarrow [2,8][/tex]

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