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What is a rational function?
- Lesson: 142:37
What is a rational function?
Lessons
For example: f(x)=x2−1x3+5x2−8x+6 ; g(x)=x2−41 ; h(x)=2x−5−8x+3
- 1.Investigating Asymptotes on the Graph of Rational Functions
Consider the rational function f(x)=x−21 .a)Complete the table of values below, then plot the points on the grid.
x
-5
-4
-3
-2
-1
0
1
2
3
4
5
y=f(x)=x−21
b)What is the non-permissible value of the rational function?c)Now, let's investigate the behaviour of the rational function near the non-permissible value by plotting more points close to the non-permissible value.
x
1.5
1.9
1.99
2
2.01
2.1
2.5
y=f(x)=x−21
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d)To investigate the right-end behaviour of the rational function (as x→∞), complete the table of values below and plot the points.
x
10
100
1000
y=f(x)=x−21
e)To investigate the left-end behaviour of the rational function (as x→−∞), complete the table of values below and plot the points.
x
-10
-100
-1000
y=f(x)=x−21