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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