Answer
Discontinuous for $x\in N$
Work Step by Step
Let $x$ be the number of pounds.
The function for $x\leq 1$ is:
$C(x) =12.8$
The function for $x\gt 1$ is
$C(x) = 12.8 + 2.5 [x-1]$.
Therefore, the combined function is
$$\begin{align*}
C(x)& = \begin{cases}
12.8 &\text{ for }x \leq 1\\
12.8 + 2.5 [x-1] &\text{ for }x \gt 1
\end{cases}
\end{align*}$$
Graph the function.
When graphed, it is clear that the function is discontinuous for $x\in N$.
