Domain: All real numbers except 7 Range: All real numbers except 0
Practice makes perfect
Let's start by recalling the general equation of a rational function.
f(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.
f(x)=- 2/x- 7+ 0
We can see that a= - 2, h= 7, and k= 0.
Therefore, the domain of the function is all real numbers except 7, the range is all real numbers except 0, and the asymptotes are the lines x= 7 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
- 2/x-7
f(x)=- 2/x-7
3
- 2/3-7
0.5
5
- 2/5-7
1
6
- 2/6-7
2
6.5
- 2/6.5-7
4
7.5
- 2/7.5-7
- 4
8
- 2/8-7
- 2
9
- 2/9-7
- 1
11
- 2/11-7
- 0.5
Let's now plot and connect the obtained points. Remember that the asymptotes are x=7 and y=0, and that the graph will have two branches.
