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Properties of Functions

Learn about the properties of functions, different ways to express them, evaluating possible functions, and understanding the concepts of domain and range. Includes exercises for practice.

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Properties of Functions

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  1. Properties of Functions Lesson 2.1

  2. Vocabulary • A function is a rule • Assigns to each element from one set • Exactly one element from another one • Another way to say it: • A set of ordered pairs where no two ordered pairs have the same first element • Think of it as a machine • Value goes in the top • Machine alters the value • Generates another value out spout 3 9

  3. Ways of Expressing a Function • A function can be reperesented by: • A table • A formula A =  r2 • A description • A graph

  4. Evaluating Possible Functions • Which is a function? • {(2,3), (4,7), (9,3)}{(2,3), (4,7), (2,9)}{(2,3), (4,7), (9,2)} Vertical Line Test

  5. Domain and Range • Domain • All the possible values of the independent variable, the set of first elements • Range • All the possible values of the dependent variable, the set of second elements

  6. Domain and Range Domain • The nature of some functions require restrictions on the domain • What must be excluded for these functions? Range

  7. Domain and Range • The nature of a function determines the extent of the range • Numbers excluded • Maximum or minimum possible values

  8. Limits on the Range • Determine the range of these functions

  9. Assignment • Lesson 2.1 • Page 66 • Exercises 1 – 71 EOO

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