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We are given a piecewise-defined function \( f(x) \) defined as:

\[
f(x) =
\begin{cases}
x, & \text{if } x \geq 0 \\
-x, & \text{if } x < 0
\end{cases}
\]

### 1. **Evaluating the function:**
Let's evaluate the function at the specified points:

- \( f(-2) \):
  Since \( -2 < 0 \), we use the second case, \( f(x) = -x \).
  \[
  f(-2) = -(-2) = 2
  \]

- \( f(0) \):
  Since \( 0 \geq 0 \), we use the first case, \( f(x) = x \).
  \[
  f(0) = 0
  \]

- \( f(1) \):
  Since \( 1 \geq 0 \), we use the first case, \( f(x) = x \).
  \[
  f(1) = 1
  \]

### 2. **Finding the domain of \( f(x) \):**
The domain of \( f(x) \) is the set of all values of \( x \) for which the function is defined. Since the function provides a rule for both \( x \geq 0 \) and \( x < 0 \), the domain of \( f(x) \) is all real numbers:
\[
\text{Domain of } f(x): (-\infty, \infty)
\]

### 3. **Sketching the graph:**

The function behaves as:
- \( f(x) = x \) for \( x \geq 0 \), which is a line with a slope of 1 passing through the origin.
- \( f(x) = -x \) for \( x < 0 \), which is a line with a slope of -1, also passing through the origin.

At \( x = 0 \), the value is \( f(0) = 0 \), so the graph is continuous at this point.

Would you like me to sketch the graph as well?

---

Here are some related questions for further practice:
1. What is the range of \( f(x) \)?
2. Is \( f(x) \) continuous at all points?
3. Find the inverse of \( f(x) \).
4. Is the function \( f(x) \) differentiable at \( x = 0 \)?
5. How does the graph of \( f(x) \) change if we modify it to \( f(x) = 2x \) when \( x \geq 0 \)?

**Tip:** For piecewise functions, always check which condition applies to a specific input before evaluating it.

Evaluate f(-2), f(0), f(1) and find the domain of the piecewise-defined function f(x) = {x if x >= 0, -x if x < 0}.

Learn how to evaluate a piecewise-defined function, f(x), at specific values of x (including -2, 0, and 1) and determine the domain of the function. This example covers algebraic concepts of piecewise functions and is suitable for students in Grades 9-12.

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