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.

Function rule is .

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

Step-by-step explanation:

Given:

So, is a transformed function of .

There are two transformations involved:

1.

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

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

2.

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.

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step-by-step explanation: