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.
y=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.
y=2/x-3 ⇔ y=2/x- 0+( - 3)
We can see that a= 2, 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
2/x-3
y=2/x-3
- 4
2/- 4-3
- 3.5
- 2
2/- 2-3
- 4
- 1
2/- 1-3
- 5
- 0.5
2/- 0.5-3
- 7
0.5
2/0.5-3
1
1
2/1-3
- 1
2
2/2-3
- 2
4
2/4-3
- 2.5
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.
