The document discusses functions and relations. It defines a relation as a set of ordered pairs and shows an example relation. It explains that a relation is a function if each x-value is mapped to only one y-value using the vertical line test. The document provides examples of function notation, evaluating functions, and graphing functions from equations. It includes examples of making tables of values and ordered pairs to graph functions.

1. Agenda 11/8
Review functions
Do Now
Homework check
Homework 4 p. 249 # 1 - 12 all
Follow all directions
Use graph paper
Quiz Friday? 5.1 - 5.4

2. 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

3. 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.

4. 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?

5. HW CHECK

6. 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

7. 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) = 7
the value of the function when x = 2

8. 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

9. input
output
RULE
x-values
domain
inputs
independent variables
y-values
range
outputs
f(x)-values
dependent variables

10. 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.

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