Analysing Rational Functionsmathlau.weebly.com/uploads/1/4/9/9/14997226/july... · 10 Chapter 9 –...
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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