Material Taken From:
Mathematics
for the international student
Mathematical Studies SL
Mal Coad, Glen Whiffen, John Owen, Robert Haese,
Sandra Haese and Mark Bruce
Haese and Haese Publications, 2004
Objectives
• To identify a cubic and a rational function
and their properties.
• To accurately graph unfamiliar functions.
• To find the solutions using the GDC.
Opening Problem
Families of Functions
Polynomial:
Linear
y=x
Rational
(a.k.a. reciprocal)
y
1
x
Polynomial:
Quadratic
y = x2
Exponential
y = 2x
Polynomial:
Cubic
y = x3
Trigonometric
y = sinx
Absolute Value
y x
Families of Functions
Polynomial:
Linear
y=x
Rational
(a.k.a. reciprocal)
y
1
x
Polynomial:
Quadratic
y = x2
Exponential
y = 2x
Polynomial:
Cubic
y = x3
Trigonometric
y = sinx
Absolute Value
y x
Things to pay attention to when graphing functions:
• x- and y- intercepts
• maxima and minima
• asymptotes, if they exist
Section 17A - Cubic Function
• www.explorelearning.com
– For demo purposes only:
• Cubic Functions
• Polynomials
Example 1
Consider the function:
y = 2x3 – 17x2 + 42x – 30
a) Find the axes intercepts
b) Find the coordinates of any turning points
c) Sketch the graph of the function, highlighting the
key features found above.
Section 17C - Rational Function
• www.explorelearning.com
– For demo purposes only:
• Rational Function
Example 2
6
Consider the function: y 
4
x2
a) Find the asymptotes of the function
b) Find the axes intercepts
c) Sketch the function, include the key features
found above.
Homework
• 17A.1 – Pg 549
– #1ach, #2ac
• 17A.3 – Pg 552
– #1bd
• 17A.4 – Pg 552-553
– #1,5
• 17C.1 – Pg 559
– #1, 3abc
• 17C.2 – Pg 561
– #1bd, 3ad
• 17C.3 – Pg 562
– #1,2
Section 17E – Unfamiliar Functions
Section 17F – Where Functions Meet
Example 3
4
Find where the line y = x – 3 meets y 
x
Accurate Graphing
• On the IB exam you will be expected to:
– draw accurate graphs of
• linear
• quadratic
• exponential and
• trigonometric functions
– use the GDC to sketch and analyze some simple
unfamiliar functions
• e.g. cubic and rational
Homework
• 17E – Pg 565
– #1
• 17F.1 – Pg 567-568
– #1ac, 2ac, 4ae, 6abc
• 17F.2 – Pg 569
– #1cf, 2ab
• IB Examples
Worksheet