Given the following graphs:
knowing that the blue one is the graph of $f$ and the orange one of $f'$, at first glance I would say that $f$ has an oblique asymptote $y = m\,x + q$, with $m = 1$ and $q < 0$, due to the horizontal asymptote of $f'$.
On the other hand, thinking about it for a moment, I think it's wrong and a counterexample should be $f(x) = x + \log x$. Am I right?
If finally, assuming that in addition to the graph there is information that $f$ admits an oblique asymptote, $q$ could only be estimated roughly from the graph, right?
Thank you!