This document defines and explains key concepts related to functions and relations, including: - Relations are sets of ordered pairs, while functions are relations where each x-value only appears once. - The domain is the set of x-values and the range is the set of y-values. To find them, list the unique x's for the domain and unique y's for the range. - The function rule is an equation that describes the relationship between x and y for a function. Examples are given of evaluating functions using the rule and finding the domain and range.

1. Relations & functions With Domain & Range

2. Relations A set of ordered pairs or a data table.

3. Function A set of ordered pairs or a data table in which the x’s don’t repeat.

4. Function? (-2, 4), (-1, 1), (0,0), (1,1), (2,4) Yes (-2, 4), (-1, 1), (0,0), (-1,1), (-2,4) No

5. Function rule An equation that describes a function

6. Example: y=3x+4 3x+4=y 4+3x=y Same equation

7. y =3 x +4 OUTput (dependent variable) INput (independent variable)

8. Function Machine

9. Function Machine

10. Terms to use x Independent Variable Input Domain y Dependent Variable Output Range

11. Domain & Range Just a list of the x’s or y’s in brackets { }. Usually from least to greatest

12. Domain & Range D={x, x, x} {list the x’s. Leave out duplicates.} R={y, y, y} {list the y’s. Leave out duplicates.}

13. Find Domain & Range (-2, 4), (-1, 1), (0,0), (1,1), (2,4) For the domain, grab the x’s D={-2, -1, 0, 1, 2} For the range, grab the y’s R={0, 1, 4}

14. Evaluate the function rule: y= x – 1 for x = -2 y= ( ) – 1 Don’t forget those ( )! y= ( -2 ) – 1 y= -3

15. Find the range for the function: When the domain is {-3, 0, 3} p = 4q – 6 y = 4x – 6 (this is the one you put in your calculator!)

16. Find the range for the function: Write it three times: y = 4( -3 ) – 6 y= y = 4( 0 ) – 6 y= y = 4( 3 ) – 6 y=

17. Find the range for the function: Make sure your stat plot is off. Go to y= and enter the equation y = 4x – 6 Enter 2 nd /Graph to get the TABLE See your answers?

18. Find the range for the function: Write it three times: y = 4( -3 ) – 6 y= -18 y = 4( 0 ) – 6 y= -6 y = 4( 3 ) – 6 y= 6

19. Review Function? Relation? Domain? Range? Function rule?