Answer: OPTION B.
Step-by-step explanation:
Below are some transformations for a function f(x):
1. If [tex]f(ax)[/tex] and [tex]a>1[/tex], the function is compressed horizontally by a factor of [tex]\frac{1}{a}[/tex].
2. If [tex]f(ax)[/tex] and [tex]0<a<1[/tex], the function is stretched horizontally by a factor of [tex]\frac{1}{a}[/tex].
3. If [tex]bf(x)[/tex] and [tex]0<b<1[/tex], the function is compressed vertically by a factor of "b".
4. If [tex]bf(x)[/tex] and [tex]b>1[/tex], the function is stretched vertically by a factor of "b".
In this case you have the function f(x):
[tex]f(x)=6^{x-2}[/tex]
And the function g(x):
[tex]g(x)=0.4(6)^{x-2}[/tex]
So, you can identify that:
[tex]g(x)=bf(x)[/tex] and [tex]0<b<1[/tex]
Therefore, the graph of the function g(x) is a vertical compression of the graph of function f(x).
