Answer
See graph
Work Step by Step
We are given some facts about our function and we are going to draw a rough graph of the function.
$\lim\limits_{x \to 0^{-}}f(x)=2$ tells us that the function (graphed as $y$) approaches $2$ as it nears $x=0$ from the left.
Similarly, $\lim\limits_{x \to 0^{+}}f(x)=0$ tells us that on the other side of $x=0$ the function approaches $0$.
We are also given the value of the function at $x=0$, $f(0)=2$.
So we know that there is a discontinuity at $x=0$ where $y$ goes from approaching $2$ to approaching $0$, which we see in the first picture.
We are also given information about the behavior of the graph at $x=4$:
$\lim\limits_{x \to 4^{-}}f(x)=3$ tells us that the function (graphed as $y$) approaches $3$ as it nears $x=4$ from the left.
$\lim\limits_{x \to 4^{+}}f(x)=0$ tells us that the function (graphed as $y$) approaches $0$ as it nears $x=4$ from the right.
We are also given the value of the function at $x=4$, $f(4)=1$.
So, at $x= 4$ the function goes from approaching $3$ from the left, equaling $1$ at $x=4$, then approaching $0$ from the right.
We can now draw out our rough graph. (see graph)
