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**Unformatted text preview: **Math Precalculus (12H/4H) Review CHSN Review Project Contents Functions 3 Polar and Complex Numbers 9 Sequences and Series 15 This review guide was written by Dara Adib. Prateek Pratel checked the “Polar and Complex Num- bers” chapter on page 9 for errors. This is a development version of the text that should be considered a work-in-progress. This review guide and other review material are developed by the CHSN Review Project. Copyright © 2008-2009 Dara Adib. This is a freely licensed work, as explained in the Definition of Free Cultural Works ( freedomdefined.org ). It is licensed under the Creative Commons Attribution- Share Alike 3.0 United States License. To view a copy of this license, visit http://creativecommons. org/licenses/by-sa/3.0/us/ or send a letter to Creative Commons, 171 Second Street, Suite 300, San Francisco, California, 94105, USA. This review guide is provided “as is” without warranty of any kind, either expressed or implied. You should not assume that this review guide is error-free or that it will be suitable for the particular purpose which you have in mind when using it. In no event shall the CHSN Review Project be liable for any special, incidental, indirect or consequential damages of any kind, or any damages whatsoever, including, without limitation, those resulting from loss of use, data or profits, whether or not advised of the possibility of damage, and on any theory of liability, arising out of or in connection with the use or performance of this review guide or other documents which are referenced by or linked to in this review guide. 2 Functions This chapter was designed for a test on functions administered by Jeanine Lennon to her Math 12H (4H/Precalculus) class on January 4, 2008. Definitions function relation in which each first coordinate (usually x value) cooresponds to only one last coor- dinate (usually y value); passes vertical line test vertical line test test on a graph to determine if a relation is a function domain set of all first coordinates (usually x values) range set of all last coordinates (usually y values) restricted domain values for which the function is undefined i.e. x | x ∈ R , x 6 = , x 6 = ± 5 inverse of a relation reversed domain and range of a relation R- 1 = { ( y , x ) } one-to-one function function whose inverse is also a function; passes both vertical and horizontal line tests periodic function function in a cycle such that f ( x + p ) = f ( x ) where p represents period amplitude 1 2 ( max- min ) of a periodic function frequency number of cycles per 360 ◦ (degrees) or 2π (radians) period duration of one cycle composite function (composition of functions) application of one function on the result of other function asymptote line that a graph approaches, but never intersects Operations on Functions Explanation ( f + g )( x ) is equivalent (and equal) to f ( x ) + g ( x ) ....

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