https://file.aiquickdraw.com/mathbot/file/1726105806998u87ielmn.jpg

Let's solve the problem using the graph provided:

### 1. Finding \( f(1) \):

From the graph, we observe the point where \( x = 1 \). The graph shows a hole (an open circle) at \( x = 1 \), and the solid point above it is located at \( y = 1 \). This point indicates that \( f(1) = 1 \).

**Answer:**
\[
f(1) = 1
\]

### 2. Finding \( \lim_{{x \to 1}} f(x) \):

To find the limit of \( f(x) \) as \( x \) approaches 1, we need to consider the behavior of the function from both the left and the right sides of \( x = 1 \).

- From the left (\( x \to 1^- \)), the function approaches \( y = 0 \).
- From the right (\( x \to 1^+ \)), the function also approaches \( y = 0 \).

Since both sides approach the same value, the limit exists.

**Answer:**
\[
\lim_{{x \to 1}} f(x) = 0
\]

Would you like further details on these calculations, or do you have any other questions? 

Here are some related questions you might find interesting:
1. What happens to \( f(x) \) as \( x \to 0 \)?
2. What is the limit of \( f(x) \) as \( x \to -1 \)?
3. Does the function \( f(x) \) have any asymptotes?
4. How would you describe the continuity of \( f(x) \) at \( x = 1 \)?
5. Can you determine \( f(x) \) at \( x = 2 \)?

**Tip:** When finding limits graphically, always observe the function's behavior from both sides of the point of interest to ensure the limit exists and is the same from both directions.

Use the graph of y = f(x) to compute the values f(1) and lim x→1 f(x). If an answer does not exist, enter DNE.

Learn how to determine the value of f(1) and compute the limit as x approaches 1 for the function f(x) using a graph. This example covers important concepts like function evaluation and limit calculation, suitable for high school students in Grades 10-12.

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