Limits Continuity And Differentiability

When $p-k \neq 0$ and $m-k \neq 0$, then $f(x)$ is continuous at $x=a$

When $p-k=0$ and $m-k \neq 0$, then $f(x)$ is left continuous at $x=a$

When $p-k \neq 0$ and $m-k=0$, then $f(x)$ is right continuous at $x=a$

When $p-m=0$ and $p-k=0$, then $f(x)$ is right continuous at $x=a$