function - PRECALCULUS THE LANGUAGE OF FUNCTIONS* In...

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THE LANGUAGE OF FUNCTIONS * In algebra you began a process of learning a basic vocabulary, grammar, and syntax forming the foundation of the language of mathematics. For example, consider the following algebraic sentence: Solve for x if 8 5 3 2 = + x x You learned to read this sentence, understand what it means, what it is asking for, and in addition, how to go about answering the question. In precalculus, it is important to learn and understand the language of functions. This includes understanding function notation and sentences using function notation. Using the language of functions, for example, we can restate the same question above in the following way: If when does 5 3 ) ( 2 + = x x x f ? 8 ) ( = x f OR If for what value(s) of x does 5 3 ) ( 2 + = x x x f 8 ) ( = x f ? OR If and for what value(s) of x does 5 3 ) ( 2 + = x x x f 8 ) ( = x g ) ( ) ( x g x f = ? OR If and when does 5 3 ) ( 2 + = x x x f 8 ) ( = x g ) ( ) ( x g x f = ? Using the language of functions, these are just a few ways to express the same question first stated above “algebraically”. What is important to note here is that the methods for finding the answer to the question may be the same as in algebra (and the process of finding the answer may be easy once you understand what is being asked): the difficult part may be understanding what is being asked. That is why it is important for you to understand functions and function notation. I. You should understand what makes an assignment a function. You should be able to identify if an assignment is a function whether the function is given as an assignment using sets, tables, ordered pairs, equations, or graphs. You should be able to identify domains (including natural domains) and ranges using sets, tables, ordered pairs, equations, or graphs. You should also know how to (and when to) use the graphing calculator to help answer questions about functions. _______________________________________ *This handout is not intended as a tutorial or a complete review of functions, but rather as a quick review of notation that we use frequently in this course. There are additional important topics such as applications, quadratic functions, extreme values, etc., which are discussed in lecture and in the text, but are not covered here . 1
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This note was uploaded on 04/13/2008 for the course PRECALC 111 taught by Professor Hirsch during the Spring '08 term at Rutgers.

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function - PRECALCULUS THE LANGUAGE OF FUNCTIONS* In...

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