1. Lesson 3-2 Functions and Function Notation Objective: To learn about functions, domains and ranges. To use function notation to represent functions

2. Functions  y = 3x + 1  For this equation, every x we choose, will give us a new y.  x is the input, and y is the output.  For every x we choose there is one and only one y possible – therefore this is a FUNCTION

3. Definition of a Function

4. Domain and Range  For each element x in X, the corresponding element y in Y is called the image of the function at x. The set X is called the domain of the function, and the set of all function values, Y is called the range of the function.

5. Ex 1: Determine whether each relation is a function.

6. Solution for part (a) 468468 578578

7. Solution for part (b) 456456 6767

8. Vertical Line Test (Pencil Test)  Given a graph – any vertical line drawn on the graph should only go through one point. Function Not a Function

9. Function Notation

11. Finding a Function’s Domain  The domain (the x’s) of a function can be almost any real number. There are two cases when there are exceptions: Division by zero – if x is in the bottom of the fraction (denominator), then x cannot make that denominator 0.  f(x) = ; x = 3 is not defined.

12. Finding a Function’s Domain Even roots of negative numbers  y = is only a real number if x ≥ 1

13. Finding a Function’s Domain

14. Ex 5: Find the domain of each function

15. Solution part a

16. Solution part b

17. Solution part c

18. Practice Exercises

19. Answers

20. Graphing Functions  Using a graphing calculator Put the equation or function into the form y = …. Button at top left y = Then type in the rest of the equation and press [GRAPH] at top right.

21. Evaluating Functions  Given f(x) = x 2 + 2x – 1, find f(2).  This means to plug in 2 wherever there is an x in the function. f(2) = (2) 2 +2(2) – 1 = 4 + 4 – 1 = 7

22. Evaluating Functions  Given f(x) = x 2 + 2x – 1, find f(–3). f(–3) = (–3) 2 +2(–3) – 1 = 9 – 6 – 1 = 2

23. Practice  f(x) = x 2 + 3x- 4, find f(-2) & f(0)  f(x) = x 2 + 1, find f(-3) & f(x-1)

24. Practice  Find the numbers for x whose image is 2. f(x) = x 2

25. HW  p 167 # 1,2,5,7,9,12,13-21 odd; 25,27,36,43,45