Chapter Review
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Identify the asymptotes. Make a table of values, then plot and connect the obtained points.
Graph:
Domain: All real numbers except -5
Range: All real numbers except 2
y=1/x+5+2 ⇔ y=1/x-( - 5)+ 2 We can see that a= 1, h= -5, and k= 2. Therefore, the domain of the function is all real numbers except -5, the range is all real numbers except 2, and the asymptotes are the lines x= -5 and y= 2. With this in mind, we will make a table of values. Be sure to include numbers on both sides of the domain.
| x | 1/x+5+2 | y=1/x+5+2 |
|---|---|---|
| - 8 | 1/- 8+5+2 | ≈ 1.67 |
| - 7 | 1/- 7+5+2 | 1.5 |
| -6 | 1/-6+5+2 | 1.8 |
| -4 | 1/-4+5+5 | 2.2 |
| -3 | 1/-3+5+2 | 2.5 |
| -2 | 1/-2+5+2 | ≈ 2.33 |
Let's now plot and connect the obtained points. Remember that the asymptotes are x=-5 and y=2, and that the graph will have two branches.
