Question

Which statement describes the graph of function g compared to function f?

Answer 1

Answer: OPTION B.

Step-by-step explanation:

Below are some transformations for a function f(x):

1. If $f(ax)$ and $a>1$, the function is compressed horizontally by a factor of $\frac{1}{a}$.

2. If $f(ax)$  and $0$, the function is stretched horizontally by a factor of $\frac{1}{a}$.

3. If $bf(x)$ and $0$, the function is compressed vertically by a factor of "b".

4. If $bf(x)$  and $b>1$, the function is stretched vertically by a factor of "b".

In this  case you have the function f(x):

$f(x)=6^{x-2}$

And the function g(x):

$g(x)=0.4(6)^{x-2}$

So, you can identify that:

$g(x)=bf(x)$ and  $0$

Therefore, the graph of the function g(x) is a vertical compression of the graph of function f(x).