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The problem asks us to graph the piecewise function \( f(x) \) defined as follows:

\[
f(x) = 
\begin{cases} 
x^2 & , \, x < 1 \\
2 & , \, x = 1 \\
-x + 1 & , \, x > 1 
\end{cases}
\]

To create the graph of \( f(x) \), let's analyze each part of this piecewise function:

1. **For \( x < 1 \)**: The function \( f(x) = x^2 \) represents a parabola. We only consider this part of the parabola for values of \( x \) less than 1. As \( x \) approaches 1 from the left, \( f(x) \to 1 \).

2. **For \( x = 1 \)**: The function has the value \( f(x) = 2 \). This is a single point at \( (1, 2) \), which we’ll plot as a dot on the graph.

3. **For \( x > 1 \)**: The function \( f(x) = -x + 1 \) is a line with a slope of -1 and a y-intercept of 1. This line only applies for \( x > 1 \).

### Graphing Strategy

- Plot the curve \( f(x) = x^2 \) for \( x < 1 \).
- Mark the point \( (1, 2) \) as an isolated point on the graph.
- Draw the line \( f(x) = -x + 1 \) for \( x > 1 \).

Would you like me to create this graph for you, or do you have any specific questions about the steps?

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### Related Questions

1. How would the graph change if \( f(x) = x^2 \) applied for \( x \leq 1 \)?
2. What happens to the function if the point at \( x = 1 \) is removed?
3. How do we determine the continuity of this piecewise function?
4. How does the slope of \( -x + 1 \) affect the graph for \( x > 1 \)?
5. What other piecewise functions involve quadratic and linear components?

### Tip

When graphing piecewise functions, make sure to mark any isolated points separately from continuous parts.

4. Gambarkan grafik fungsi f(x) = { x^2 , x < 1; 2 , x = 1; -x + 1 , x > 1 }

Learn how to graph the piecewise function f(x), defined as f(x) = x^2 for x < 1, f(x) = 2 for x = 1, and f(x) = -x + 1 for x > 1. This solution includes a step-by-step breakdown of graphing quadratic and linear segments and analyzing piecewise continuity. Ideal for high school students in Grades 10-12.

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