Question

WILL MARK BRAINLINEST, WORTH 25 POINTS Given f(x)=3^(x-2) and g(x)=f(3x)+4, write the function rule for function g and describe the types of transformations that occur between function f and function g.

Answer 1

Function rule is
`g(x)=f(x)\rightarrow f(3x)\rightarrow f(3x)+4`.

The transformations are compression in the x direction by a factor of 3 and then vertically shifting up by 4 units.

Explanation:

Given:

`f(x)=3^(x-2)`

`g(x)=f(3x)+4`

So,
`g(x)` is a transformed function of
`f(x)`.

There are two transformations involved:

1.
`f(x)\rightarrow f(3x)`

The
`x` value of the function
`f(x)` is multiplied by 3. So, according to transformation rules, when the
`x` value of the function
`f(x)` is multiplied by a positive number greater than 1, then the function compresses in the x direction.

As 3 is multiplied to
`x`,
`f(x)` will be compressed in the x direction by a factor of 3.

2.
`f(3x)\rightarrow f(3x) +4`

Now, 4 is added to the compressed function. As per transformation rules, when a positive number is added to a given function, the function has a vertical shift.

Here, the compressed function will shift vertically up by 4 units.