4
MHF4U-B
Transformations of
Exponential and
Logarithmic Graphs
Lesson 4, page 1
Advanced Functions MHF4U-B
Introduction
Up to this point in the unit, you have looked at the basic graphs
of quadratic, exponential, and logarithmic functions. In this
lesson

3
MHF4U-B
Graphs of Logarithmic
Functions
Lesson 3, page 1
Advanced Functions MHF4U-B
Introduction
You can probably recite the alphabet without even thinking
about it, but can you do it backward? On the other hand, you are
likely able to give directions f

8
MHF4U-B
Rational Functions
Lesson 8, page 1
Advanced Functions MHF4U-B
Introduction
You are aware that certain operations are not defined or are
impossible in mathematics. One of these operations is division by
4
zero. For example,
is undefined. Why doe

9
MHF4U-B
Factor Theorem
Lesson 9, page 1
Advanced Functions MHF4U-B
Introduction
When was the last time you did a division question such
as 632 17125 without a calculator? Long division is a skill
that is not practised much since calculators are so readi

MHF4U-B
2
Unit
Polynomial and Rational Functions
Copyright 2012 The Ontario Educational Communications
Authority. All rights reserved. No part of these materials may
be reproduced, in whole or in part, in any form or by any means,
electronic or mechanical

5
MHF4U-B
Exponential and
Logarithmic Equations
Lesson 5, page 1
Advanced Functions MHF4U-B
Introduction
How long does it take for a given amount of a radioactive
substance to decay until it is considered safe? How much more
powerful was an earthquake in

7
MHF4U-B
Transformations of
Polynomial Functions
Lesson 7, page 1
Advanced Functions MHF4U-B
Introduction
You have studied many different functions in this course and in
other mathematics courses. You learned that it was possible to
alter or transform th

10
MHF4U-B
Solving Inequalities
Lesson 10, page 1
Advanced Functions MHF4U-B
Introduction
A variety of events can be modelled with mathematical
equations. For example, falling objects can be modelled by
quadratic equations. It is often possible to model r

2
MHF4U-B
Introduction to Logarithms
Lesson 2, page 1
Advanced Functions MHF4U-B
Introduction
Scientists such as chemists, astronomers, and geologists are
often confronted with either extremely large or extremely
small numbers. A chemist may work with che

1
MHF4U-B
Exponents and Exponential
Functions
Lesson 1, page 1
Advanced Functions MHF4U-B
Introduction
Mathematics has been around from the early beginnings of
society. Shepherds in ancient times needed to count in order to
keep track of tribal members, p