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Question

Part 1
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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​(Type integers or simplified fractions. Type N if the function is​ undefined.)

Answer 1

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 $x$.

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 $x=2$:
   $f(2)=\frac{1}{2-2}$ is undefined. So, we will write N (not defined).

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 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!