Graph the piecewise function below by first selecting whether the endpoints are included in the graph or not, then drag the endpoints of the lines to the correct locations.

f(x)={|x|ifx<23ifx≥2

We are tasked with graphing the piecewise function \( f(x) \) which is defined as:

\[
f(x) =
\begin{cases} 
|x| & \text{if } x < 2 \\
3 & \text{if } x \geq 2
\end{cases}
\]

### Step-by-step breakdown:

1. **First part of the piecewise function**: \( f(x) = |x| \) for \( x < 2 \)
   - The function \( |x| \) represents the absolute value of \( x \). 
   - For \( x < 2 \), the function will graph as a V-shape with the vertex at \( (0, 0) \).
   - Since \( x = 2 \) is **not included** in this part (because it's strictly \( x < 2 \)), there will be an **open circle** at \( (2, |2|) = (2, 2) \) to indicate that the endpoint is not included.
   
2. **Second part of the piecewise function**: \( f(x) = 3 \) for \( x \geq 2 \)
   - For \( x \geq 2 \), the function value is constantly 3.
   - At \( x = 2 \), \( f(x) = 3 \), so we place a **closed circle** at \( (2, 3) \) to show that this point is included.
   - The graph will be a horizontal line extending to the right from \( (2, 3) \).

### Final Graph:
- For \( x < 2 \), plot the V-shaped graph of \( |x| \), with an open circle at \( (2, 2) \).
- For \( x \geq 2 \), plot a horizontal line at \( f(x) = 3 \), with a closed circle at \( (2, 3) \).

Would you like me to generate the visual graph for you, or is there any part you'd like further clarification on?

### Related Questions:
1. What is the domain of the function \( f(x) \)?
2. How do you find the range of a piecewise function?
3. What does an "open circle" on a graph represent?
4. How do you graph the absolute value function \( |x| \)?
5. How do you graph horizontal lines on a coordinate plane?

### Tip:
Always carefully observe the inequalities in piecewise functions to determine if endpoints are included or not.

Graph the piecewise function below by first selecting whether the endpoints are included in the graph or not, then drag the endpoints of the lines to the correct locations.

f(x)={|x|ifx<23ifx≥2

Learn how to graph the piecewise function f(x) = |x| for x < 2 and f(x) = 3 for x ≥ 2. This problem demonstrates key concepts in graphing absolute value functions and constant functions with endpoint inclusion rules. Suitable for students in Grades 9-12.

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