Show that $$f(x) = \begin{cases}\displaystyle{4x-5}&\text{if}\ x < 10\cr \displaystyle{\frac{1}{x+8}}&\text{if}\ x \ge 10\end{cases}$$ has a jump discontinuity at $10$ by calculating the limit as $x$ approaches 10 from the left and from the right.

$\displaystyle{\lim_{x\to 10^-}f(x)} =$

$\displaystyle{\lim_{x\to 10^+}f(x)} =$

Now draw a graph of $f$.