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.
h(x)=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.
h(x)=- 3/x+2 ⇔ h(x)=- 3/x-( - 2)+ 0
We can see that a= - 3, 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
- 3/x+2
h(x)=- 3/x+2
- 8
- 3/- 8+2
0.5
- 5
- 3/- 5+2
1
- 4
- 3/- 4+2
1.5
- 3
- 3/- 3+2
3
- 1
- 3/- 1+2
- 3
0
- 3/0+2
- 1.5
1
- 3/1+2
- 1
4
- 3/4+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.
