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We are given the function \( f(x) = \frac{x}{x - 4} \) and are asked to find the function values for \( f(-2) \), \( f(0) \), and \( f(3) \), indicating if the function is undefined at any point.

Let's solve each case one by one:

### 1. \( f(-2) \)
Substitute \( x = -2 \) into the function:
\[
f(-2) = \frac{-2}{-2 - 4} = \frac{-2}{-6} = \frac{1}{3}
\]
So, \( f(-2) = \frac{1}{3} \).

### 2. \( f(0) \)
Substitute \( x = 0 \) into the function:
\[
f(0) = \frac{0}{0 - 4} = \frac{0}{-4} = 0
\]
So, \( f(0) = 0 \).

### 3. \( f(3) \)
Substitute \( x = 3 \) into the function:
\[
f(3) = \frac{3}{3 - 4} = \frac{3}{-1} = -3
\]
So, \( f(3) = -3 \).

### Conclusion:
- \( f(-2) = \frac{1}{3} \)
- \( f(0) = 0 \)
- \( f(3) = -3 \)

You can now match the corresponding values to the boxes.

Would you like any further explanation, or do you have other questions?

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Here are 5 related questions to deepen your understanding:
1. What happens if \( x = 4 \) in the given function?
2. How do you determine where a rational function is undefined?
3. Can you explain why \( f(x) = \frac{x}{x-4} \) has a vertical asymptote at \( x = 4 \)?
4. What is the behavior of the function as \( x \) approaches 4 from both sides?
5. How would you graph \( f(x) = \frac{x}{x - 4} \)?

**Tip:** Always check for values that make the denominator zero, as these indicate points where the function may be undefined.

Find the function values for f(-2), f(0), and f(3) for the function f(x) = x / (x - 4).

Learn how to solve the rational function f(x) = x / (x - 4) by finding values of f(-2), f(0), and f(3). This problem includes key concepts in rational functions and substitution, suitable for students in Grades 9-11.

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