Step-by-step explanation
Jillian is incorrect because the shown graph is not a radical function but a logarithmic function instead. Both radical and logarithmic increase for f(x) when x increases as well.
Note that radical functions do not have any asymptotes, that includes vertical and horizontal.
The shown graph is a logarithmic function. The name already says it. The logarithmic function is part of logarithmic where the equation is

Answer
- Part A — Jillian is incorrect. The graph has vertical asymptote at x = 0, and radical functions do not have vertical asymptote.
- Part B — logarithmic