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.

---

Let $f(x) = \begin{cases}\displaystyle{x^{2}+3x+7}&\text{if}\ x < 10\cr \displaystyle{16}&\text{if}\ x = 10\cr \displaystyle{-3x+4}&\text{otherwise}\end{cases}$
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 $f(x)$.