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

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1.1Functions and Their Usein ModellingStudent Text Pages 6 to 22T 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 SEnsure students are comfortable with the function notations and terminologyintroduced. The ability to describe functions flexibly, following the rule of fourand employing descriptions such as domain, range, symmetry, and piecewise, iscritical to students’ success in the course.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.Use the latter part of the section to get students used to mathematical modellingas a process. Regression of data against linear, polynomial, and exponentialmodels is used both to introduce and to validate these functions as models,a role they play constantly in subsequent chapters.Question 17inApply, Solve, Communicatemakes a good journal assignment.It can then be used as a homework quiz the next day.There is anAchievement Checkat 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 thetechniques, time spent now in practice and additional instruction is a good invest-ment for the remainder of the course. Students who are more comfortable withthis 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 MyxnThe properties of the power functions explored include the shapes and symmetriesof their graphs. Common features of power functions with even and odd exponentsare also examined.S a m p l e R e s p o n s e s1. a)An appropriate range foryfor 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 they-axis.d)The common points are (1, 1), (0, 0), and (1, 1).2. a)An appropriate range foryfor the three functions is [30, 5] with steps of 5.b)The graphs are curves that open downward.1.1Functions and Their Use in Modelling• MHR3Technologygraphing calculators orgraphing softwareRelated ResourcesMcGraw-Hill RyersonCalculus & Advanced FunctionsPractice/Assessment Masters:1.1Solutions:1.1Computerized AssessmentBank:1.1Student e-bookcontent:Car Depreciation:An Exponential Model:The solution to part d)of Example 8 isdemonstrated usingTI InterActive!™.Teacher’s ResourceCD-ROM:List data files (for Examples1, 7; questions 9, 11, 12,18–22)AssessmentAchievement CheckSpecific ExpectationsDetermine, throughinvestigation, using graphingcalculators or graphingsoftware, various propertiesof the graphs of polynomialfunctions.

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