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Calculus I - Notes Review : Functions

Technically a student coming into a Calculus class is supposed to know both Algebra and Trigonometry.  The reality is often much different however.  Most students enter a Calculus class woefully unprepared for both the algebra and the trig that is in a Calculus class.  This is very unfortunate since good algebra skills are absolutely vital to successfully completing any Calculus course and if your Calculus course includes trig (as this one does) good trig skills are also important in many sections.

 

The intent of this chapter is to do a very cursory review of some algebra and trig skills that are absolutely vital to a calculus course.  This chapter is not inclusive in the algebra and trig skills that are needed to be successful in a Calculus course.  It only includes those topics that most students are particularly deficient in.  For instance factoring is also vital to completing a standard calculus class but is not included here.  For a more in depth review you should visit my Algebra/Trig review or my full set of Algebra notes at http://tutorial.math.lamar.edu.

 

Note that even though these topics are very important to a Calculus class I rarely cover all of these in the actual class itself.  We simply don’t have the time to do that.  I do cover certain portions of this chapter in class, but for the most part I leave it to the students to read this chapter on their own.

 

Here is a list of topics that are in this chapter.  I’ve also denoted the sections that I typically cover during the first couple of days of a Calculus class.

 

Review : Functions  Here is a quick review of functions, function notation and a couple of fairly important ideas about functions.

 

Review : Inverse Functions  A quick review of inverse functions and the notation for inverse functions.

 

Review : Trig Functions  A review of trig functions, evaluation of trig functions and the unit circle.  This section usually gets a quick review in my class.

 

Review : Solving Trig Equations  A reminder on how to solve trig equations.  This section is always covered in my class.

 

Review : Solving Trig Equations with Calculators, Part I  The previous section worked problems whose answers were always the “standard” angles.  In this section we work some problems whose answers are not “standard” and so a calculator is needed.  This section is always covered in my class as most trig equations in the remainder will need a calculator.

 

Review : Solving Trig Equations with Calculators, Part II  Even more trig equations requiring a calculator to solve.

Review : Exponential Functions  A review of exponential functions.  This section usually gets a quick review in my class.

 

Review : Logarithm Functions  A review of logarithm functions and logarithm properties.  This section usually gets a quick review in my class.

 

Review : Exponential and Logarithm Equations  How to solve exponential and logarithm equations.  This section is always covered in my class.

 

Review : Common Graphs  This section isn’t much.  It’s mostly a collection of graphs of many of the common functions that are liable to be seen in a Calculus class.

 

Calculus I - Notes Review : Functions

Online Notes / Calculus I (Notes) / Review

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