Domain: All real numbers except - 7 Range: All real numbers except - 5
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=10/x+7-5 ⇔ y=10/x-( - 7)+( - 5)
We can see that a= 10, h= - 7, and k= - 5.
Therefore, the domain of the function is all real numbers except - 7, the range is all real numbers except - 5, and the asymptotes are the lines x= - 7 and y= - 5.
With this in mind, we will make a table of values. Be sure to include numbers on both sides of the domain.
x
10/x+7-5
y=10/x+7-5
- 17
10/- 17+7-5
- 6
- 12
10/- 12+7-5
- 7
- 9
10/- 9+7-5
- 10
- 8
10/- 8+7-5
- 15
- 6
10/- 6+7-5
5
- 5
10/- 5+7-5
0
- 2
10/- 2+7-5
- 3
3
10/3+7-5
- 4
Let's now plot and connect the obtained points. Remember that the asymptotes are x=- 7 and y=- 5, and that the graph will have two branches.
