Answer
Explanation
The first condition f(1) = 0 means that when x = 1, y = 0, which is represented in the following part of the graph:
Next, we are told that at f(3) is undefined. In this case, this is represented by the empty dot when x = 3. The empty dot means it is undefined in this function (graph below, red circle).
The following condition:
[tex]\lim_{x\to3}f(x)=1[/tex]
Is saying that when x approaches the 3 value, y = 1 which is also represented in the graph by the blue line:
The next condition states that when x approaches 0 from the positive side, y approaches –∞ (red arrow shown in the graph below):
[tex]\lim_{x\to0^+}f(x)=-\infty[/tex]
Similarily,
[tex]\lim_{x\to2}f(x)=\infty[/tex]
states that when x approaches 2, y approaches ∞ (yellow arrow shown in the graph below):
Finally,
[tex]\lim_{x\to4}f(x)=\infty[/tex]
states that when x approaches 4, y approaches ∞ (red arrow shown in the graph below):
