2. Relations & Functions An Introduction for Algebra Students

3. November 2001Created by Cathy Stevens 2 A relation is any set of ordered pairs. {(x, y), (-5, 6), (4, 7), (6, 8)}

4. November 2001 Created by Cathy Stevens3 Relations can be written in different ways As a list of coordinate points… {(3,1), (-4,5), (5,0)} As a table of values… As an equation… y = 3x-1 As a graph… x 1 2 3 y 2 4 6

5. November 2001Created by Cathy Stevens 4 The domain of a relation is all the first coordinates of the ordered pairs. {(0, -2), (3, 1), (3, 5), (8,-4)} Domain: {0, 3, 8}

6. November 2001Created by Cathy Stevens 5 The range is all the second coordinates in a relation. {(0, -2), (3, 1), (3, 5), (7, -9)} Range: {-2, 1, 5, -9}

7. November 2001 Created by Cathy Stevens6 Check out this machine! Input Output

8. November 2001 Created by Cathy Stevens7 Think of a relation in terms of input and output Input, x 035035 -2 1 5 6 Output, y

9. November 2001 Created by Cathy Stevens8 The Vocabulary of Relations  X  Input  Domain  Range  Output  y

10. November 2001Created by Cathy Stevens 9 A function is a relation in which no two ordered pairs have the same x- value. {(2, -3), (4, 5), (6, 5), (7,9)}

11. November 2001 Created by Cathy Stevens10 Examine these relations to see if they are functions.  {(0, -3), (2, 5), (4, 7), (5, -8)} Function?  {(2, 4), (5, 3), (5, -7)} Function?

12. November 2001 Created by Cathy Stevens11 Are these relations functions? {(2, 4), (3, 4), (5, -7)} {(3, -2), (3, 5), (6, 4)} x 3 4 4 y 0-2-4 Input 3 7 8 Output 0-4

13. November 2001 Created by Cathy Stevens12 The Real Function Machine f(x)= 3x + 5 f(1)= 3(1) + 5 = 3 + 5 = 8 Input x Output f(x)

14. November 2001 Created by Cathy Stevens13 The Vertical Line Test  A relation is a function in which no vertical line crosses its graph in more than one point.

15. November 2001 Created by Cathy Stevens14 Use the vertical line test Function?

16. November 2001 Created by Cathy Stevens15 Challenge  Write three relations, one in each format. Ordered Pairs A table (T-chart) A graph  Challenge a classmate to determine which relations are functions.