which graph of f(x) satisfies these conditions? lim x→2− f(x)=−4 and lim x→2+ f(x)=0
which graph of f(x) satisfies these conditions? lim x→2− f(x)=−4 and lim x→2+ f(x)=0
Answer
Explanation:
Step1: Understand left - hand limit
The left - hand limit $\lim_{x\rightarrow2^{-}}f(x)= - 4$ means as $x$ approaches 2 from the left side, the function $f(x)$ approaches - 4. We need to check the value of the function on the left - hand side of $x = 2$ for each graph.
Step2: Understand right - hand limit
The right - hand limit $\lim_{x\rightarrow2^{+}}f(x)=0$ means as $x$ approaches 2 from the right side, the function $f(x)$ approaches 0. We check the value of the function on the right - hand side of $x = 2$ for each graph.
Step3: Analyze graphs
For the first graph, as $x$ approaches 2 from the left, $y$ approaches - 4 and as $x$ approaches 2 from the right, $y$ approaches 0.
Answer:
The first graph.