Let

$$f(x) = \begin{cases} mx+3 & \text{if } x < 3 \\ m+n & \text{if } x = 3 \\ -x+9 & \text{if } x > 3 \end{cases}$$

a. Find

$$\lim_{x \rightarrow 3^-} f(x)$$

and

$$\lim_{x \rightarrow 3^+} f(x)$$

b. Find the

$$\lim_{x \rightarrow 3} f(x) = f(3)$$

c. Find the value of $m$ and $n$ such that $f(x)$ is continuous at $x = 3$

d. After finding the values of $m$ and $n$, sketch the graph of the function.