investigation – key features of rational functions

A rational function has the form , where and are polynomials.

The domain of a rational function is the set of all real numbers except the zeros of the

denominator,. That is,  0. Otherwise the rational function would be undefined.

1.Sketch the graphs below. Label the asymptotes.

2.Complete the table below.

Domain
Range
Eqn of Vertical Asymptote
Eqn of Horizontal Asymptote
Positive
Intervals
Negative Intervals
Increasing Interval
Decreasing Interval
Zero(s)

3.For the function for k R, predict the:

Domain: ______Range: ______

Eqn of Vertical Asymptote: ______Eqn of Horizontal Asymptote: ______

4.Sketch the graphs. Label the asymptotes.


x / y
-12
-2
0
2
2.5
3.6
4
6
15
/
x / y
-12
-2
0
2
2.2
3.8
4
9
18
/
x / y
-16
-11
-6
-1.5
-1.2
-0.8
0
9
19
/
x / y
-16
-11
-6
-2
-1.4
-0.8
0
9
19

5.Complete the table below.

Domain
Range
Eqn of Vertical Asymptote
Eqn of Horizontal Asymptote
Positive
Intervals
Negative
Intervals
Increasing
Interval
Decreasing
Interval
Zero(s)

6.Without sketching, complete the table below:

Domain
Range
Eqn of Vertical Asymptote
Eqn of Horizontal Asymptote
Zero(s)

7.In general, for the function for k R and n R, predict the following:

Domain: ______Range: ______

Eqn of Vertical Asymptote: ______Eqn of Horizontal Asymptote: ______

Zero(s) ______

8.Sketch the graphs.


x / y
-8
-3
-1
1
1.8
2.2
3
5
/
x / y
-7
-3
-2.1
-1.9
-1
0
3
8
/
x / y
-16
-14
-10
-8
-7
-5
-4
2
4
10
/
x / y
-19
-10
-2
2
4
5.6
6.5
8
14
16

9.Complete the table below.

Domain
Range
Eqn of Vertical Asymptote
Eqn of Horizontal Asymptote
Positive
Intervals
Negative
Intervals
Increasing
Interval
Decreasing
Interval
Zero(s)

10.Without sketching, complete the table below:

Domain
Range
Eqn of Vertical Asymptote
Eqn of Horizontal Asymptote
Zero(s)

11.In general, for the function for p  R, n R and k R, predict the following:

Domain: ______Range: ______

Eqn of Vertical Asymptote: ______Eqn of Horizontal Asymptote: ______

Zero(s) ______