Agenda 11/8

Review functions

Do Now

Homework check

Homework 4 p. 249 # 1 - 12 allFollow all directionsUse graph paper

Quiz Friday? 5.1 - 5.4

5.2 RELATIONS AND FUNCTIONS 11/8

Relation a set of ordered pairs

it can be expressed as:

Ordered Pairs

(-1, 1)

(0, 2)

(1, 3)

(2, 4)

Table

x

x

2

Mapping

-1 1

0 2

1 3

2 4

Graph

y

-1 1

0 2

1 3

4

The Vertical Line Test

Otherwise known as the stupid pencil trick!If a vertical line intersects more than one point on a graph, it is not a function. An x-value cannot have 2 different y-values.

Do Now

RELATION: (1, 4) (-2, 3) (0, 3) (1, 2)

Please show this relation in these ways:

TABLE MAPPING GRAPH

Is this a function? Why or why not?

HW CHECK

22. 9

23. -16.5

24. 6 2/3

25. -5.25

26. 90

27. 28

28. 17.6

29. 67.5

30. 700

31. 105.6 km

32. 0.5

33. 8 11/12

34. 7 1/3

35. - 3 1/2

36. 8

37. 165

p. 185 # 22 - 37

Function Notation

y = 3x - 4

f(x) = 3x - 4

}

EQUIVALENT

f(x) = "the f of x" - what you do to x

f(x) = 4x - 1

f(2) = ? -- 4(2) -1 = 7 f(2) = 7the value of the function when x = 2

PRACTICE

f(x) = x + 2; f(3) = ?5

f(x) = x3 + 4; f(2) = ?12

g(x) = 2x - 1; g(-2) = ?-5

f(x) = -x2 + 5; f(-2) = ?1

f(x) = x + 1; g(x) = 2x;f(g(3)) = ?7

input

outputRULE

x-valuesdomaininputsindependent variables

y-valuesrangeoutputsf(x)-valuesdependent variables

EQUATIONS AS FUNCTIONS

When a function is written as an equation, we can make a graph.

example: y = 2x + 1

1. Make a table and choose input values (x).

x y (x, y)y = 2x + 1

2. Fill in table to get ordered pairs.

3. Graph ordered pairs and make a line.

y = x - 2

x y (x, y)y = x - 2

y = 1/3 x - 2

x y (x, y)y = 1/3 x - 2