choose the graph that meets all three of the following requirements: lim f(x) = 3 lim f(x) = -1 lim f(x) = 2

Explanation:

Step1: Analyze left - hand limit at $x = 1$

The left - hand limit $\lim_{x\rightarrow1^{-}}f(x)=3$ means as $x$ approaches 1 from the left, the function value approaches 3.

Step2: Analyze right - hand limit at $x = 1$

The right - hand limit $\lim_{x\rightarrow1^{+}}f(x)= - 1$ means as $x$ approaches 1 from the right, the function value approaches - 1.

Step3: Analyze limit at $x = 4$

The limit $\lim_{x\rightarrow4}f(x)=2$ means as $x$ approaches 4, the function value approaches 2. We check each graph for these conditions.

Answer:

You need to visually inspect each of the four graphs provided. Look for a graph where as $x$ approaches 1 from the left, the $y$ - value approaches 3; as $x$ approaches 1 from the right, the $y$ - value approaches - 1; and as $x$ approaches 4, the $y$ - value approaches 2. Without the ability to label the graphs (A, B, C, D), I can't specify which one it is, but you should use the above limit - based criteria to make the selection.