Domain: All real numbers except 0 Range: All real numbers except 3
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)=4/x- 0+ 3
We can see that a= 4, h= 0, and k= 3.
Therefore, the domain of the function is all real numbers except 0, the range is all real numbers except 3, and the asymptotes are the lines x= 0 and y= 3.
With this in mind, we will make a table of values. Be sure to include numbers on both sides of the domain.
x
4/x+3
g(x)=4/x+3
- 4
4/- 4+3
2
- 2
4/- 2+3
1
- 1
4/- 1+3
- 1
1
4/1+3
7
2
4/2+3
5
4
4/4+3
4
Let's now plot and connect the obtained points. Remember that the asymptotes are x=0 and y=3, and that the graph will have two branches.
