Question

Find a function, g(x) that transform f (x) = 3 sqrt x by shifting f (x) right 3 units

Answer 1

Given

The function is

`f(x)=3√(x)`

The function g(x) transform by shifting f(x) right 3 units.

To find:

The function g(x).

Explanation:

The translation is defined as

`g(x)=f(x+a)+b`

where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

The function f(x) shifts only 3 units right. So,

`a=-3,b=0`

Now,

`g(x)=f(x+(-3))+0`

`g(x)=f(x-3)`

`g(x)=3√(x-3)`
`[\because f(x)=3√(x)]`

Therefore, the required function is
`g(x)=3√(x-3)`.