1. Objectives The student will be able to: 1. To determine if a relation is a function. 2. To find the value of a function.

2. 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

3. Function Notation Output Input Name of Function

4. Determine whether each relation is a function. 1.{(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

5. Determine whether the relation is a function. 2. {(4, 1), (5, 2), (5, 3), (6, 6), (1, 9)} f(x)f(x) 41 f(x)f(x) 52 f(x)f(x) 53 f(x)f(x) 66 f(x)f(x) 19 NO, 5 is paired with 2 numbers!

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

7. 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!

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

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

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

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

12. Given g(x) = x 2 – 2, find g(4) Answer Now 1.2 2.6 3.14 4.18

13. 4.4 Objective - To represent functions using models, tables, graphs, and equations. Function - A rule that describes a dependent relationship between two quantities. Domain - The set of input values in a function. Range - The set of output values in a function.

14. 0 1 2 3 4 5 6 7 Let n = # of trianglesLet p = the perimeter of each figure n p 13 24 35 46 57 68 Dependent Model: Table:Graph:Equation: p n # of triangles perimeter 8765432187654321 p = n + 2 Dependent Line is discrete Discrete data is counted

15. Discrete data usually occurs in a case where there are only a certain number of values, or when we are counting something (using whole numbers). Continuous data makes up the rest of numerical data. This is a type of data that is usually associated with some sort of physical measurement.

16. Let n = # of hexagons Let p = perimeter of figure n p 16 210 314 418 522 626 Dependent Model: Table:Graph:Equation: 0 1 2 3 4 5 6 7 p n # of hexagons perimeter 30 25 20 15 10 5 p = Dependent Line is discrete 4n + 2

17. This chart shows the price of sliced fruit platters. 1) How much would a 6 lb. platter cost? 1.50 $8.10 + 1.50 = $ 9.60 2) Write an equation for the cost of a platter that weighs w lbs. Let p = price of platter p = 1.50 w +0.60 3) How much would a 10 lb. platter cost? p = 1.50 w + 0.60 p = 1.50 ( 10 ) + 0.60 p = 15.00 + 0.60 = $15.60 ChangeStart Value

18. A taxi cab charges a flat rate of $2.50 and 15 c per mile. Write a linear equation for the charge in terms of the number of miles driven. Let C = charge in dollars Let m = # of miles driven C = 2.50 + 0.15 m ChangeStart Value

19. A phone company charges $17.50 per month and 12 c for each additional minute. Write a linear equation for the charge in terms of the number of minutes. Let C = charge in dollars Let m = # of minutes C = 17.50 + 0.12 m ChangeStart Value

20. m Let m = # of minutes Let V = Volume of gas in tank V = 5 + 1.6m V 0 2 4 6 8 10 5 8.2 11.4 14.6 17.8 21 30 25 20 15 10 5 Line is continuous A car’s fuel tank is filled at a rate of 1.6 gal/min. The tank held 5 gallons of gas before refueling. Volume of gas in tank 0 2 4 6 8 10 12 # minutes Table: Graph: Equation: Continuous data is measured