1. 2.1 Domain and Range of Functions

2. Vocabulary ● Relation – A relation is a general term for any set of ordered pairs. ● Function – A function is a special type of relation in which each member of the domain is paired with exactly one member of the range. ● Domain – The domain is the set of all x-coordinates in a set of ordered pairs. ● Range – The range is the set of all y-coordinates in a set of ordered pairs.

3. Name the Domain and Range The following set of ordered pairs has a limited number of points. Ex:{(2,3),(-1,0),(2,-5),(0,-3)} Domain: Range: *If a number occurs more than once, you do not need to list it more than one time.

4. Name the Domain and Range From a Graph Domain:{all real numbers} Range:{y:y≥0} The set of ordered pairs may be an infinite number of points as described by a graph.

5. Find the Domain and Range The set of ordered pairs may be an infinite number of points as described by an equation. Find the domain and range of What limits do we have for x? x - 5 must be a positive value so x – 5 > 0. What limits do we have for y? Square roots are always positive. Domain: Range:

6. Functions A function is a relation in which each element of the domain is paired with exactly one element of the range. Another way of saying it is that there is one and only one output (y) with each input (x). f(x)f(x) x y

7. Function Notation Output Input Name of Function

8. Determine whether the relation is a function. {(2, 3), (3, 0), (5, 2), (4, 3)} YES, every domain is different! f(x)f(x) 23 f(x)f(x) 30 f(x)f(x) 52 f(x)f(x) 43

9. Determine whether the relation is a function. {(4, 1), (5, 2), (5, 3), (6, 6)} f(x)f(x) 41 f(x)f(x) 52 f(x)f(x) 53 f(x)f(x) 66 NO, 5 is paired with 2 numbers!

10. Is this relation a function? {(1,3), (2,3), (3,3)} 1. Yes 2. No Answer Now

11. Vertical Line Test (pencil test) If any vertical line passes through more than one point of the graph, then that relation is not a function. Are these functions? FUNCTION! NOPE!

12. Vertical Line Test NO WAY! FUNCTION! NO!

13. Is this a graph of a function? 1. Yes 2. No Answer Now

14. Given f(x) = 3x - 2, find: 1) f(3) 2) f(-2) 3(3)-2 3 7 3(-2)-2 -2-8 = 7 = -8

15. Given h(z) = z 2 - 4z + 9, find h(-3) (-3) 2 -4(-3)+9 -330 9 + 12 + 9 h(-3) = 30

16. Given g(x) = x 2 – 2, find g(-4) Answer Now 1. 2 2. 6 3. 14 4. 18

17. Given f(x) = 2x + 1, find -4[f(3) – f(1)] Answer Now 1. -40 2. -16 3. -8 4. 4

18. 1. {(3,7),(-3,7),(7,-2),(-8,-5)} 2. 3. 4. D: {-8,-3,3,7} R: {-5,-2,7} Find the Domain and Range of the Following Sets of Ordered Pairs D: {x: x > 3} R: {All Reals} D: {All Reals} R: {y > -4} D: {x: x 0} R: {y: y 0}