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

Answer:

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

Range: [2,8]

Step-by-step 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]

Answer 2

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.