Final answer:
Based on the given graph below the correct local behaviors are: As x → ∞, f(x) → 2 and As x → -∞, f(x) → -2.
The answer is option ⇒1 and 2
Step-by-step explanation:
Based on the given graph of the rational function f(x), we can determine the local and end behaviors by observing the behavior of the graph as x approaches different values.
From the graph, we can see that as x approaches positive infinity (∞), f(x) approaches 2. This means that as x becomes very large, the values of f(x) get closer and closer to 2. Therefore, the statement "As x → ∞, f(x) → 2" is correct.
Similarly, as x approaches negative infinity (-∞), f(x) approaches -2. This means that as x becomes very large in the negative direction, the values of f(x) get closer and closer to -2. Therefore, the statement "As x → -∞, f(x) → -2" is also correct.
However, we cannot determine the behavior of f(x) as x approaches 3 from the graph provided. The graph does not show any specific behavior around x = 3. Therefore, the statement "As x → 3, f(x) → [infinity]" cannot be determined from the given graph.
Additionally, we cannot determine the behavior of f(x) as x approaches 0. The graph does not show any specific behavior around x = 0. Therefore, the statement "As x → 0, f(x) → -14" cannot be determined from the given graph.
In conclusion, based on the given graph:
- The correct local behaviors are: As x → ∞, f(x) → 2 and As x → -∞, f(x) → -2.
The answer is option ⇒1 and 2
Your question is incomplete, but most probably the full question was:
Check Picture
The graph of the rational function f(x) is shown below. Using the graph, determine which of the following local and end behaviors are correct.
As x → ∞, f(x) → 2
As x → -∞, f(x) → -2.
As x → 3, f(x) →∞
As x → 0, f(x) → -14