Chapter 9 – Rational Functions ● 9

Pre-Calculus 12

Analysing Rational Functions

Example 1: Sketch the graph 3

9)(

2

−

−=

x

xxf . Analyse the its behaviour near the non-permissible value.

Example 2: Analyse the function and predict the location of any vertical asymptotes, points of discontinuity,

and intercepts. Then graph the function to verify your predictions.

86

42

+−

−=

xx

xy

10 ● Chapter 9 – Rational Functions

Pre-Calculus 12

Example 3: Match the equation of each rational function with the most appropriate graph. Explain your

reasoning.

2

2)(

2

2

−−

+=

xx

xxK

1

1)(

2−

−=

x

xxL

x

xxxM

−

+−=

3

65)(

2

To match, the equation of functions with their graphs, use the location(s) of points of discontinuity,

asymptotes, and intercepts. Write each equation in factored form.

Assignment: worksheet

Chapter 9 – Rational Functions ● 11

Pre-Calculus 12

Connecting Graphs and Rational Equations Solving with a Graphing Calculator

Example 1: Solve the equation 123

732

−=

−

−−x

x

xx

Method 1: Use of a single function.

Method 2: Use of a system of two functions.

[ , ] [ , ]

[ , ] [ , ]

12 ● Chapter 9 – Rational Functions

Pre-Calculus 12

Example 2: Solve the equation 104

1582

52 +

+=+

+ x

xx

x

xalgebraically.

Assignment: page 465-466 #3-7, 9