Domain: All real numbers except 4 Range: All real numbers except - 1
Practice makes perfect
Let's start by recalling the general equation of a rational function.
g(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.
g(x)=- 3/x-4-1 ⇔ g(x)=- 3/x- 4+( - 1)
We can see that a= - 3, h= 4, and k= - 1.
Therefore, the domain of the function is all real numbers except 4, the range is all real numbers except - 1, and the asymptotes are the lines x= 4 and y= - 1.
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-4-1
g(x)=- 3/x-4-1
1
- 3/1-4-1
0
2
- 3/2-4-1
0.5
3
- 3/3-4-1
2
5
- 3/5-4-1
- 4
6
- 3/6-4-1
- 2.5
7
- 3/7-4-1
- 2
Let's now plot and connect the obtained points. Remember that the asymptotes are x=4 and y=- 1, and that the graph will have two branches.
