A function $f(x)$ is said to have a jump discontinuity at $x=a$ if:
1. $\displaystyle{ \lim_{x\to a^-}f(x)}$ exists.
2. $\displaystyle{ \lim_{x\to a^+}f(x)}$ exists.
3. The left and right limits are not equal.

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Let $f(x) = \begin{cases} 4 x - 5, &\text{if}\ x<10\\ \frac{1}{x+8}, &\text{if}\ x\geq 10 \end{cases}$
Show that $f(x)$ has a jump discontinuity at $x=10$ by calculating the limits from the left and right at $x=10$.
$\displaystyle{ \lim_{x\to 10^-}f(x)}=$
$\displaystyle{ \lim_{x\to 10^+}f(x)}=$
Now, for fun, try to graph $f(x)$.