Answer:
Function rule is [tex]g(x)=f(x)\rightarrow f(3x)\rightarrow f(3x)+4[/tex].
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:
[tex]f(x)=3^{x-2}[/tex]
[tex]g(x)=f(3x)+4[/tex]
So, [tex]g(x)[/tex] is a transformed function of [tex]f(x)[/tex].
There are two transformations involved:
1. [tex]f(x)\rightarrow f(3x)[/tex]
The [tex]x[/tex] value of the function [tex]f(x)[/tex] is multiplied by 3. So, according to transformation rules, when the [tex]x[/tex] value of the function [tex]f(x)[/tex] is multiplied by a positive number greater than 1, then the function compresses in the x direction.
As 3 is multiplied to [tex]x[/tex], [tex]f(x)[/tex] will be compressed in the x direction by a factor of 3.
2. [tex]f(3x)\rightarrow f(3x) +4[/tex]
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.
