Answer
$F$
Work Step by Step
In order to find out the correct answer, we must follow the following points:
(a) If the function has a horizontal asymptote of $y=a$ and is below the asymptote, this shows the equation has the form of: $y=m-3^n$.
(b) If the function has a horizontal asymptote of $y=a$ and is above the asymptote, this shows the equation has the form of: $y=m+3^n$.
(c) The graph of $y=f(x-h)$ represents a horizontal shift, when $h \gt 0$, of $|h|$ units to the right and to the left when $h\lt 0$ of the original function $f(x)$.
(d) The exponent of $3$ is positive when the graph is increasing, and it is negative when the graph is decreasing.
So, we can see from the depicted graph that the function is $y=3^x$ shifted 1 unit to the right, which is $y=3^{x-1}$. It has a horizontal asymptote of $x=0$, is increasing and positive (above the horizontal asymptote) with points $f(0)=\dfrac{1}{3}, f(1)=1$.
Therefore, $F$ is the correct answer.
