Question

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.

Answer 1

Answer:

Function rule is $g(x)=f(x)\rightarrow f(3x)\rightarrow f(3x)+4$.

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:

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

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

So, $g(x)$ is a transformed function of $f(x)$.

There are two transformations involved:

1. $f(x)\rightarrow f(3x)$

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

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

2. $f(3x)\rightarrow f(3x) +4$

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.