1. Objective: 1-1 Relations and Functions 1 SAT/ACT Practice  1. What is the sum of the positive even factors of 12?

2. 2 What you will learn  How to determine whether a given relation is a function  How to identify the domain and range of a function  How to evaluate a function

3. Objective: 1-1 Relations and Functions 3 Relations and Functions? 1.49 2.98 31.47 41.96 52.45 62.94 73.43 This is an example of a relation. A relation is simply a pairing of elements. The first element is called the domain. The second element is called the range.

4. Objective: 1-1 Relations and Functions 4 An Example  State the relation of the following windchill data as a set of ordered pairs. Also state the domain and range of the relation. 519 103 15-5 20-10 25-15 30-18 Wind spd. Windchill temp.

5. Objective: 1-1 Relations and Functions 5 Limiting the Domain of a Function  Why? Because we want to. The domain of a relation is all positive integers less than 6. The range y of the relation is 3 less x, where x is a member of the domain. Write the relation as a table of values and as an equation. Graph the relation.

6. Objective: 1-1 Relations and Functions 6 Determining Domain and Range of Relations  When a relation is graphed, you can determine the domain and range by “looking at” the graph. Examples on graphing calc.  Remember: Domain is the “possible” x values and range is the “possible” y values.

7. Objective: 1-1 Relations and Functions 7 A Function  Sometimes, a relation is actually a function.  A function is a relation in which each element of the domain is paired with exactly one element in the range.  How can you tell? Look at x and corresponding y values Vertical line test

8. Objective: 1-1 Relations and Functions 8 Is it a function?  (-3, 2), (-5, 3), (-1, 2), (-3, 3)  (-1, 5), (9, 3), (3, 2), (-1, 5)

9. Objective: 1-1 Relations and Functions 9 Is it a function?

10. Objective: 1-1 Relations and Functions 10 Is it a function?

11. Objective: 1-1 Relations and Functions 11 Is it a function?

12. Objective: 1-1 Relations and Functions 12 Function Notation…huh?  y = 3x + 5 is the same thing as f(x) = 3x + 5.  We can use f(x) notation instead of y (or h(t) or s(f) or…)

13. Objective: 1-1 Relations and Functions 13 Evaluating Functions  Evaluate each function for the given value: 1. f(-4) if f(x) = 3x 3 – 7x 2 – 2x 2. g(9) if g(x) = |6x – 77|

14. Objective: 1-1 Relations and Functions 14 Evaluating Functions with Variables Instead of Numbers  Evaluate h(a) if h(x) = 3x 7 – 10x 4 + 3x – 11  Evaluate j(c – 5) if j(x) = x 2 – 7x + 4

15. Objective: 1-1 Relations and Functions 15 You Try  Evaluate h(a-2) if h(x) = 2x 2 – x + 3

16. Objective: 1-1 Relations and Functions 16 Values of the Domain  Some values of x may cause a “problem” and they need to be excluded from the possible values of x.  y=3x + 4any problems?  What about:

17. Objective: 1-1 Relations and Functions 17 Homework Section 1.1  Page 10, 18, 24, 26, 34, 40, 42, 44, 48, 57