The graph where I based my answers:
I am trying to determine where my two mistakes are.
Based in the graph, the following are my answers:
1. $f(0) = 0$
There is a dot in the graph at the origin. I assume that it is the function value.
2. $f(2) = \text{DNE}$
When $x$ is equal to $2$, the function value cannot be determined because both sides are approaching different infinities. Therefore, it does not exist.
3. $f(3) = \text{DNE}$
I am not sure in this one. Because first of all, there is no dot. So I first assumed that it is equal to positive infinity. Could it be $0$ or positive infity?
4. $\lim\limits_{x \to -1} = \text{DNE}$
The left hand and the right hand limit are not equal. Therefore, it does not exist.
5. $\lim\limits_{x \to 0} f(x) = 0$
Both the left and right hand limits approach exactly at the origin.
6. $\lim\limits_{x \to 2^+} f(x) = -\infty$
It is very obvious from the graph itself.
7. $\lim\limits_{x\to +\infty} f(x) = +\infty$
I am not sure in this one. Could it be DNE?
Where did I go wrong?