Question

Complete the table of values for the following function and then plot the points to graph the function by hand.
​f(x)equalsStartFraction 1 Over x minus 2 EndFraction
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Part 1
x
minus2
minus1
0
1
2
3
4
​f(x)equalsStartFraction 1 Over x minus 2 EndFraction
  
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Answer 1

To complete the table of values for the function \( f(x) = \frac{1}{x - 2} \), we will substitute each value of \( x \) from the list into the function to find \( f(x) \).

Here are the calculations:

1. **For \( x = -2 \)**:
\[
f(-2) = \frac{1}{-2 - 2} = \frac{1}{-4} = -\frac{1}{4}
\]

2. **For \( x = -1 \)**:
\[
f(-1) = \frac{1}{-1 - 2} = \frac{1}{-3} = -\frac{1}{3}
\]

3. **For \( x = 0 \)**:
\[
f(0) = \frac{1}{0 - 2} = \frac{1}{-2} = -\frac{1}{2}
\]

4. **For \( x = 1 \)**:
\[
f(1) = \frac{1}{1 - 2} = \frac{1}{-1} = -1
\]

5. **For \( x = 2 \)**:
The function is undefined at \( x = 2 \) since it results in division by zero.

6. **For \( x = 3 \)**:
\[
f(3) = \frac{1}{3 - 2} = \frac{1}{1} = 1
\]

7. **For \( x = 4 \)**:
\[
f(4) = \frac{1}{4 - 2} = \frac{1}{2}
\]

Now, assembling these values gives us the completed table:

| \(x\) | \(f(x)\) |
|:-------:|:-----------:|
| -2 | -0.25 |
| -1 | -0.33 |
| 0 | -0.5 |
| 1 | -1 |
| 2 | Undefined |
| 3 | 1 |
| 4 | 0.5 |

### Summary of the Values:
- \( f(-2) = -0.25 \)
- \( f(-1) = -0.33 \)
- \( f(0) = -0.5 \)
- \( f(1) = -1 \)
- \( f(2) \) is undefined
- \( f(3) = 1 \)
- \( f(4) = 0.5 \)

You can now plot these points on a graph to visualize the function. Here’s how they should look:

- **Points for plotting**:
- (-2, -0.25)
- (-1, -0.33)
- (0, -0.5)
- (1, -1)
- (3, 1)
- (4, 0.5)

Make sure to indicate that there is a vertical asymptote at \( x = 2 \) since the function is undefined at this point.