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:
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For \( x = -2 \): \[ f(-2) = \frac{1}{-2 - 2} = \frac{1}{-4} = -\frac{1}{4} \]
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For \( x = -1 \): \[ f(-1) = \frac{1}{-1 - 2} = \frac{1}{-3} = -\frac{1}{3} \]
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For \( x = 0 \): \[ f(0) = \frac{1}{0 - 2} = \frac{1}{-2} = -\frac{1}{2} \]
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For \( x = 1 \): \[ f(1) = \frac{1}{1 - 2} = \frac{1}{-1} = -1 \]
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For \( x = 2 \): The function is undefined at \( x = 2 \) since it results in division by zero.
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For \( x = 3 \): \[ f(3) = \frac{1}{3 - 2} = \frac{1}{1} = 1 \]
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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.
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