Logarithmic functions / asymptotes

Basic concepts

5.3.nb

Asymptotes

  • The graph of $f(x)$ has a horizontal asymptote of $y=a$ if $$\lim_{x\to\infty}=a \text{ or }\lim_{x\to -\infty}=a$$ if $f\to a$ far away from the origin.
  • The graph of $f(x)$ has a vertical asymptote of $x=a$ if $$\lim_{x\to a^+}=+\infty \text{ or }\lim_{x\to a^-}=+\infty \text{ or } \lim_{x\to a^+}=-\infty \text{ or }\lim_{x\to a^-}=-\infty $$ if the function "blows up" as $x\to a$.