Hello again, symmetry!
Okay, here's an example.
. . $\displaystyle f(x) \:=\:\begin{Bmatrix}3 & \text{if }0 \leq x \leq 1 \\ 2x + 1 & \text{if }x > 1\end{Bmatrix}$
When $\displaystyle x$ is between $\displaystyle 0$ and $\displaystyle 1$ (including the endpoints),
. . the graph is $\displaystyle f(x) = 3$, a horizontal line. Code:

3* * * * *


 +    +  
 1
When $\displaystyle x$ is greater than 1, the graph is $\displaystyle f(x) \:=\:2x + 1$,
. . a slanted line. Code:

 *
 *
 *
 *
3 *


 +    +       
 1
Sketch them on the same graph
. . and have the graph of the piecewise function. Code:

 *
 *
 *
 *
3o * * * *


 +    +       
 1
This function could be your longdistance charge.
They might charge $3 for the first minute
. . and $2 per minute for every subsequent minute.
(Hmmm, not a good example . . .
I'm sure someone will point out why.)