Answer:
Here's a possible example:
Step-by-step explanation:
[tex]f(x) =\begin{cases} x & \quad x < 3\\x+3 & \quad x \geq 3\\\end{cases}[/tex]
Each piece is linear, so the pieces are continuous by themselves.
We need consider only the point at which the pieces meet (x = 3).
[tex]\displaystyle \lim_{x \longrightarrow 3^{-}} f(x) = \lim_{x \longrightarrow 3^{-}} x = 3\\\\\displaystyle \lim_{x \longrightarrow 3^{+}} f(x) = \lim_{x \longrightarrow 3^{+}} x+3 = 6\\\\f(3) = x + 3 = 6\\\\\displaystyle \lim_{x \longrightarrow 3^{-}} f(x) \neq f(3)[/tex]
The left-hand limit does not equal ƒ(x), so there is a jump discontinuity at x =3.
