1. Chapter 5 Section 1 Introduction to Functions

2. Rules of Correspondence • We often use a rule to relate how the first value of an ordered pair relates to the second one. Rule x y Domain Range

3. Definition of a Relation • A Relation maps a value from the domain to the range. A Relation is a set of ordered pairs. • The most common types of relations in algebra, map subsets of real numbers to other subsets of real numbers.

4. Definition of a Function • If a relation has the additional characteristic that each element of the domain is mapped to one and only one element of the range then we call the relation a Function.

6. Relation? (A) (B) • 46 mpg • 8 mpg • 106 mpg (C)

7. X Y 1 1 -5 1 -1 1 3 1 X Y 1 2 -5 7 -1 2 3 3 X Y 1 2 1 7 1 2 1 3 X Y 1 1 π 2 π 1 -1 5 π 3 Examples • Decide if the following relations are functions.

10. Vertical Line Test • If a vertical line crosses a graph more than once, then the graph is not a function.

11. X Y 1 2 5 10 -1 -2 3 6 Ways to Represent a Function • Graphical • Algebraic • Numeric • DescriptiveThe cost is twice the original amount.

12. Pieces of a Function • A function consists of 3 parts:1. a set of objects called the domain2. a second set of objects called the range3. And a rule that describes how to assign a unique range object to each object in the domain.

13. Name of the function • Output Value• Member of the Range• Dependent Variable These are all equivalent names for the y. • Input Value• Member of the Domain• Independent Variable These are all equivalent names for the x. Function Notation

14. Use This!

15. Your Turn

17. Domain Issues • Cannot take the square root of a negative number • Cannot divide by 0

18. Your Turn

19. Review Quiz • Given the ordered pairs P(–1, 2) and Q(–3, 5), find the equation of the line through these points in Slope-Intercept form.