Question

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.

Answer 1

Answer with Step-by-step explanation:

We are given that

$f(x)=3^{x-2}$

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

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

$(x,y)\rightarrow (3x,y)$

Then, we get $h(x)=f(3x)=3^{3x-2}$

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

Then, the translation rule is given by

$(x,y)\rightarrow (x,y+4)$

Then , we get

$g(x)=3^{3x-2}+4$