Questions: Lesson: 10.1 One-Sided Limits Question 1 of 16, Step 1 of 4 Use the graph of y=f(x) to find the limits: Step 1 of 4: Find lim x→-3^+ f(x).

Transcript text: Lesson: 10.1 One-Sided Limits Question 1 of 16, Step 1 of 4 Use the graph of $y=f(x)$ to find the limits: Step 1 of 4: Find $\lim _{x \rightarrow-3^{+}} f(x)$.

Solution

Solution Steps

Step 1: Understand the Problem

We need to find the limit of the function $ f(x) $ as $ x $ approaches 3 using the given graph.

Step 2: Analyze the Graph

Examine the behavior of the function $ f(x) $ as $ x $ approaches 3 from both the left and the right.

Step 3: Determine the Left-Hand Limit

Observe the value that $ f(x) $ approaches as $ x $ approaches 3 from the left (denoted as $ x \to 3^- $).

Step 4: Determine the Right-Hand Limit

Observe the value that $ f(x) $ approaches as $ x $ approaches 3 from the right (denoted as $ x \to 3^+ $).

Step 5: Compare the Left-Hand and Right-Hand Limits

If the left-hand limit and the right-hand limit are equal, then the limit exists and is equal to this common value. If they are not equal, the limit does not exist.

Final Answer

From the graph, as $ x $ approaches 3 from the left, $ f(x) $ approaches 5. As $ x $ approaches 3 from the right, $ f(x) $ also approaches 5. Therefore, the limit of $ f(x) $ as $ x $ approaches 3 is:

\[ \lim_{{x \to 3}} f(x) = 5 \]

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