Questions: Describe the local behavior of the function shown in the graph above. As x approaches -4 from the left, f(x) approaches Select an answer As x approaches -4 from the right, f(x) approaches Select an answer Describe the long run behavior of the function shown in the graph above. As x approaches infinity, f(x) approaches Select an answer As x approaches negative infinity, f(x) approaches Select an answer

Describe the local behavior of the function shown in the graph above.
As x approaches -4 from the left, f(x) approaches Select an answer
As x approaches -4 from the right, f(x) approaches Select an answer
Describe the long run behavior of the function shown in the graph above.
As x approaches infinity, f(x) approaches Select an answer
As x approaches negative infinity, f(x) approaches Select an answer

Transcript text: Describe the local behavior of the function shown in the graph above. As $x \rightarrow-4^{-}, f(x) \rightarrow$ Select an answer As $x \rightarrow-4^{+}, f(x) \rightarrow$ Select an answer Describe the long run behavior of the function shown in the graph above. As $x \rightarrow \infty, f(x) \rightarrow$ Select an answer As $x \rightarrow-\infty, f(x) \rightarrow$ Select an answer

Solution

Solution Steps

Step 1: Analyze the local behavior as x approaches -4 from the left

As $ x \to -4^- $, the function $ f(x) $ approaches $ -\infty $. This is because the graph shows that as $ x $ gets closer to -4 from the left, the function value decreases without bound.

Step 2: Analyze the local behavior as x approaches -4 from the right

As $ x \to -4^+ $, the function $ f(x) $ approaches $ \infty $. This is because the graph shows that as $ x $ gets closer to -4 from the right, the function value increases without bound.

Step 3: Describe the long run behavior as x approaches infinity

As $ x \to \infty $, the function $ f(x) $ approaches $ -1 $. This is because the graph shows that as $ x $ increases towards infinity, the function value levels off and approaches the horizontal asymptote at $ y = -1 $.