To compute the values of the function \( f(x) = \frac{1}{x - 2} \) for the given x-values, we will evaluate the function for each \( x \).
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For \( x = -2 \):
\( f(-2) = \frac{1}{-2 - 2} = \frac{1}{-4} = -\frac{1}{4} \) -
For \( x = -1 \):
\( f(-1) = \frac{1}{-1 - 2} = \frac{1}{-3} = -\frac{1}{3} \) -
For \( x = 0 \):
\( f(0) = \frac{1}{0 - 2} = \frac{1}{-2} = -\frac{1}{2} \) -
For \( x = 1 \):
\( f(1) = \frac{1}{1 - 2} = \frac{1}{-1} = -1 \) -
For \( x = 2 \):
\( f(2) = \frac{1}{2 - 2} \) is undefined. So, we will write N (not defined). -
For \( x = 3 \):
\( f(3) = \frac{1}{3 - 2} = \frac{1}{1} = 1 \) -
For \( x = 4 \):
\( f(4) = \frac{1}{4 - 2} = \frac{1}{2} \)
Now we can summarize the table of values:
| \( x \) | \( f(x) \) | |---------|-------------------------| | -2 | -\(\frac{1}{4}\) | | -1 | -\(\frac{1}{3}\) | | 0 | -\(\frac{1}{2}\) | | 1 | -1 | | 2 | N | | 3 | 1 | | 4 | \(\frac{1}{2}\) |
Summary of Results:
- \( f(-2) = -\frac{1}{4} \)
- \( f(-1) = -\frac{1}{3} \)
- \( f(0) = -\frac{1}{2} \)
- \( f(1) = -1 \)
- \( f(2) = N \) (undefined)
- \( f(3) = 1 \)
- \( f(4) = \frac{1}{2} \)
Graphing the Points:
On a coordinate system, you can plot the points:
- (-2, -1/4)
- (-1, -1/3)
- (0, -1/2)
- (1, -1)
- (3, 1)
- (4, 1/2)
Note on the function:
The function has a vertical asymptote at \( x = 2 \), which means that the function approaches infinity or negative infinity as \( x \) approaches 2 from the left or right. Thus, in a graph, there will be a break at that point.
You can sketch the graph based on these points and the characteristics of the function!
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