Domain: All real numbers except - 2 Range: All real numbers except 0
Practice makes perfect
Let's start by recalling the general equation of a rational function.
y=a/x- h+ k
The domain of this type of function is all real numbers except h. The range is all real numbers except k.
The asymptotes are the lines x= h and y= k. Let's now identify the values of a, h, and k for the given function.
y=1/x+2 ⇔ y=1/x-( - 2)+ 0
We can see that a= 1, h= - 2, and k= 0.
Therefore, the domain of the function is all real numbers except - 2, the range is all real numbers except 0, and the asymptotes are the lines x= - 2 and y= 0.
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+2
y=1/x+2
- 4
1/- 4+2
- 0.5
- 3
1/- 3+2
- 1
- 2.5
1/- 2.5+2
- 2
- 1.5
1/- 1.5+2
2
- 1
1/- 1+2
1
0
1/0+2
0.5
Let's now plot and connect the obtained points. Remember that the asymptotes are x=- 2 and y=0, and that the graph will have two branches.
