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# Lecture 3.1 bt

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### Lecture 3.1 bt

1. 1. Today’s Agenda  Attendance / Announcements ◦ Projects due ◦ No Quiz Friday (exam week) ◦ Need Graphing Calculators (TI-83,84,..)  Section 3.1
2. 2. Functions A function is a rule (think: operation) that assigns an input value to exactly one specific output f(x) can be thought of as “y”
3. 3. Examples…before we really define what a function is. 32 xy 32)( xxf xxy 323 2 ttth 323)( 2 xy 3 xxg 3)(
4. 4. A function is a rule (think: operation) that assigns an input value to exactly one specific output inputs outputsf(x) Domain Range
5. 5. Determine if each relation is a function or not… 9 4 1 0 1 4 9 3 2 1 0 - 1 - 2 - 3 “Functions need to be predictable!”
6. 6. Determine if each relation is a function or not… -2 -1 0 3 4 6 9 3 2 1 0 1 2 3 Since it is a function, it has a domain and range: Domain (set of all inputs): { } Range (set of all outputs): { }
7. 7. Function Notation (p. 137)
8. 8. Evaluating Functions ,2)( 2 xxxfif )3(f )3(f )(tf )3( xf
9. 9. “The Difference Quotient” The difference quotient for a function f(x) is: h xfhxf )()( Substitute, Subtract, and Simplify
10. 10. h xfhxf )()( Find the difference quotient of: 53)( xxf
11. 11. h xfhxf )()( Find the difference quotient of: 53)( xxf
12. 12. h xfhxf )()( Find the difference quotient of: 1)( 2 xxf
13. 13. Finding Domains of Functions The domain of a function is the set of values where the function is defined. So, to find domains, we need to think about where functions are NOT defined!
14. 14. Finding Domains of Functions Red Flags • Zero(s) in the denominator • Negative under square root
15. 15. Finding Domains of Functions
16. 16. Finding Domains of Functions
17. 17. Finding Domains of Functions
18. 18. Classwork / Homework Page 140 9 – 19 odd, 23 – 29 odd, 35 – 45 odd, 51