Chapter 9 – Rational Functions ● 9 Pre-Calculus 12 Analysing Rational Functions Example 1: Sketch the graph 3 9 ) ( 2 − − = x x x f . 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. 8 6 4 2 + − − = x x x y
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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