https://file.aiquickdraw.com/mathbot/file/1726622931018mb3g2zn0.jpg

From the image, we are tasked with analyzing the graph of the function \( f(x) \) to evaluate some one-sided limits and verify a statement.

### 1. The First Limit:
The limit as \( x \) approaches \( 0^- \) (from the left) is already provided:
\[
\lim_{{x \to 0^-}} f(x) = 2
\]
This means as \( x \) approaches 0 from the left, the function value approaches 2, which matches the graph's behavior near \( x = 0 \).

### 2. The Second Limit:
We now need to determine:
\[
\lim_{{x \to 0^+}} f(x)
\]
Looking at the graph, as \( x \) approaches 0 from the right, the function value still seems to approach \( 2 \) (there’s no break or jump near \( x = 0 \) on the right side). Therefore:
\[
\lim_{{x \to 0^+}} f(x) = 2
\]

### 3. Statement Verification:
The next task is to determine whether the statement
\[
\lim_{{x \to 0}} f(x) = 2
\]
is **True** or **False**. Since both the left-hand limit (\( x \to 0^- \)) and the right-hand limit (\( x \to 0^+ \)) are equal to 2, the overall limit exists and is equal to 2. Thus, the statement is **True**.

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Would you like further details or clarification?

Here are five related questions to expand your understanding:
1. What happens to \( f(x) \) when \( x \to 4^- \) and \( x \to 4^+ \)?
2. How can you determine if a function is continuous at a point using limits?
3. What is the relationship between one-sided limits and the overall limit?
4. How can you identify discontinuities in a graph based on limits?
5. What is the difference between limits that exist and limits that do not?

**Tip**: When analyzing limits graphically, always check the function's behavior from both sides of the point in question to ensure the left-hand and right-hand limits match.

Analyze the graph of the function f(x) to evaluate one-sided limits and determine whether the statement lim(x → 0) f(x) = 2 is true or false.

Learn how to analyze a function graphically to evaluate one-sided limits and verify continuity. This problem covers key calculus concepts of one-sided limits and continuity. Suitable for high school students in Grades 11-12.

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