Domain: All real numbers except 1 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)=6/x- 1+ 0
We can see that a= 6, h= 1, and k= 0.
Therefore, the domain of the function is all real numbers except 1, the range is all real numbers except 0, and the asymptotes are the lines x= 1 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
6/x-1
h(x)=6/x-1
- 5
6/- 5-1
- 1
- 2
6/- 2-1
- 2
- 1
6/- 1-1
- 3
0
6/0-1
- 6
2
6/2-1
6
3
6/3-1
3
4
6/4-1
2
7
6/7-1
1
Let's now plot and connect the obtained points. Remember that the asymptotes are x=1 and y=0, and that the graph will have two branches.
