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


Let $\displaystyle {f{{\left({x}\right)}}}={\left\lbrace\begin{array}{ccc} {8}{x}-{7}&\text{if}&{x}<{4}\\{\frac{{{1}}}{{{x}+{4}}}}&\text{if}&{x}\geq{4}\end{array}\right.}$
Show that $\displaystyle {f{{\left({x}\right)}}}$ has a jump discontinuity at $\displaystyle {x}={4}$ by calculating the limits from the left and right at $\displaystyle {x}={4}$.
$\displaystyle \lim_{{{x}\to{4}^{{-}}}}\ \ {f{{\left({x}\right)}}}=$Preview Question 6 Part 1 of 2  
$\displaystyle \lim_{{{x}\to{4}^{+}}}\ \ {f{{\left({x}\right)}}}=$Preview Question 6 Part 2 of 2  
Now for fun, try to graph $\displaystyle {f{{\left({x}\right)}}}$.