Answer:
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:
![f(x)=3^{x-2}](https://tex.z-dn.net/?f=f%28x%29%3D3%5E%7Bx-2%7D)
![g(x)=f(3x)+4](https://tex.z-dn.net/?f=g%28x%29%3Df%283x%29%2B4)
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. ![f(3x)\rightarrow f(3x) +4](https://tex.z-dn.net/?f=f%283x%29%5Crightarrow%20f%283x%29%20%2B4)
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.