Chapter1.pdf - 01-Calculus12TR-Chap01 5/23/02 2:29 PM 1.1...

1.1 Functions and Their Use
in Modelling
Student Text Pages 6 to 22
T E A C H I N G A N D A S S E S S M E N T S U G G E S T I O N S
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Ensure students are comfortable with the function notations and terminology
introduced. The ability to describe functions flexibly, following the rule of four
and employing descriptions such as domain, range, symmetry, and piecewise, is
critical to students’ success in the course.
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Likewise, practice with interval notation at this stage will help students through-
out the course, where interval descriptions are key to the analysis of functions.
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Use the latter part of the section to get students used to mathematical modelling
as a process. Regression of data against linear, polynomial, and exponential
models is used both to introduce and to validate these functions as models,
a role they play constantly in subsequent chapters.
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Question 17 in Apply, Solve, Communicate makes a good journal assignment.
It can then be used as a homework quiz the next day.
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There is an Achievement Check at the end of the section.
Concepts such as those introduced in Chapters 3 and 4 will be difficult for stu-
dents to grasp unless they have a certain level of comfort with basic function skills.
Therefore, if students seem lacking in confidence or have difficulty applying the
techniques, time spent now in practice and additional instruction is a good invest-
ment for the remainder of the course. Students who are more comfortable with
this early material could act as study partners to help with this process.
I N V E S T I G AT E & I N Q U I R E :
F U N C T I O N S I N T H E F O R M y x n
The properties of the power functions explored include the shapes and symmetries
of their graphs. Common features of power functions with even and odd exponents
are also examined.
S a m p l e R e s p o n s e s
1. a) An appropriate range for y for the three functions is [ 5, 30] with steps of 5.
b) The graphs are curves that open upward.
c) The graphs are symmetric with respect to the y -axis.
d) The common points are ( 1, 1), (0, 0), and (1, 1).
2. a) An appropriate range for y for the three functions is [ 30, 5] with steps of 5.
b) The graphs are curves that open downward.
1.1 Functions and Their Use in Modelling • MHR
3
Technology
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graphing calculators or
graphing software
Related Resources
McGraw-Hill Ryerson
Calculus & Advanced Functions
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Practice/Assessment Masters: 1.1
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Solutions: 1.1
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Computerized Assessment
Bank: 1.1
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Student e-book content:
– Car Depreciation:
An Exponential Model:
The solution to part d)
of Example 8 is
demonstrated using
TI InterActive!™.
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Teacher’s Resource CD-ROM:
– List data files (for Examples
1, 7; questions 9, 11, 12,
18–22)
Assessment
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Achievement Check
Specific Expectations
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Determine, through
investigation, using graphing
calculators or graphing
software, various properties
of the graphs of polynomial
functions.