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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. See attached for proper functions.

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Answer with Step-by-step explanation:

We are given that

[tex]f(x)=3^{x-2}[/tex]

[tex]g(x)=f(3x)+4[/tex]

We have to write the rule for function g and describe the transformation between f and g.

Compress the function by scale factor 3 and the translation rule is given by

[tex](x,y)\rightarrow (3x,y)[/tex]

Then, we get [tex]h(x)=f(3x)=3^{3x-2}[/tex]

Now, shift the y coordinate 4 units above the origin.

Then, the translation rule is given by

[tex](x,y)\rightarrow (x,y+4)[/tex]

Then , we get

[tex]g(x)=3^{3x-2}+4[/tex]

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