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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. 1 -14 Ņ 0 Select all correct answers. Select all that apply: Asx - 3*, f(x) → [infinity] As x co, f(x) → -2 Asx oo, f(x) → 2 Asx-00, f(x) --2 As x 37. f(x) → -[infinity] As x → -[infinity]o, f(x) → 2

User Yari
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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

The graph of the rational function f(x) is shown below. Using the graph, determine-example-1
User Caleb Kester
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