1. Introduction to Functions 3 January 2011

2. Definition Function – a set (of points, an equation, or a graph) where each domain (input) has exactly one range (output)

3. Method #1 – Mapping When you use it: Ordered Pairs (points) or a Table 1. Create 2 columns – Domain (input or x-values) and Range (output or y-values) 2. List all the possible inputs in the domain column and all the possible outputs in the range column

4. Method #1 – Mapping 3. Draw arrows from each domain value to the appropriate range value 4. If each domain value has only one arrow → Function 5. If one or more domain value has more than one arrow → Not a Function

5. Example #1 {(1, 5), (3, 5), (5, 7), (7, 8), (9, 5)} DomainRange

6. Example #2 DomainRange Input11233 Output56789

7. Your Turn: Complete problems 1 – 8 on the Introduction to Functions Practice Handout

8. Method #2 – Solving for a Unique Value for y When you use it: Equations Solve for y. (Get the equation in the from y = ) Hints: If y has a positive and a negative solution (ex. y = ±2x), then the equation is not a function Absolute value → Not a function y raised to even powers → Not a function y raised to odd powers (including 1) → Function

9. Example #1 4x – 2y 3 + 5 = 0

10. Example #2 y 2 – x + 1 = 0

11. Example #3 10 = | x 2 – y |

12. Your Turn: Complete problems 9 –15 on the Introduction to Functions Practice Handout

13. Method #3: Vertical Line Test When you use it: Graphs Sweep a vertical line over the graph from left to right If the graph intersects the vertical line only once at any point on the graph → Function If the graph ever intersects the vertical line more than once at any point on the graph → Not a Function

14. Example #1: y = | x |

15. Example #2: y 2 = x

16. Your Turn: Complete problems 16 – 21 on the Introduction to Functions Practice Handout