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Now go to the class site and
take the determining functions
mini quiz
The domain is the set of all of the inputs (x values) for a function
The range is the set of all of the outputs (y values) for a function
Now go to the class site and take
the mini quiz on
domain and range
Try It!
2
Given the function y = 2x + 4
and the domain [0=-2,3,4,1],
find the range of the function
2
2(-2) + 4 = 12
2(3) + 4 = 22
2(4) + 4 = 36
2(1) + 4 = 6
2
R = [12,22,36,6]
Determining
Values
Given the domain of a function and the function rule, it is possible to determine the range by
plugging the domain values into the rule
Example
Given the function rule y = 4x + 8,
give the range when the domain is
[3,4,5]
y = 4(3) +5
y = 17
y = 4(4) + 5
y = 21
y = 4(5) + 5
y = 25
R= [17,21,25]
Try It!
2
Given the function y = 2x + 4
and the domain [0=-2,3,4,1],
find the range of the function
Example
Is the following relation a function?
[(4,8), (3,8), (5,8), (7,8)]
Yes, there are no repeated x values, so the relation is a function
A relation is a rule that changes an input into an output
What is a Relation?
Relations can be shown in a number of ways
[(0,1), (3,6), (5,7)]
A set of ordered pairs
x
0
3
5
y
1
6
7
A table
A Graph
(x,y)
Called:
x-coordinate
input
abcissa
Called:
y-coordinate
output
ordinate
What is a Function?
A function is a special relation in which there is only one output (y) for
each input (x)
Determining if a graph is a function
Use the Vertical Line Test
Now go to the class site and take the evaluating functions mini quiz
To determine from a set of ordered pairs or table, simply check to make sure there are no repeated x values
[(2,7), (4,8), (3,7), (5,6)]
y
3
5
7
9
x
2
3
2
4
Function
Not a function
Try It!
Is the following relation a function?
[(4,8), (3,8), (5,8), (7,8)]
Try It!
Is this a graph of
a function?
Domain and Range
Try It!
State the domain
and range of
the graph
Try It!
Is this a graph of
a function?
State the domain and range of the function
Example
No, it does not pass
the vertical line test
[(3,4),(4,5),(7,10),(15,6)]
Domain: [3,4,7,15]
Range: [4,5,10,6]
Functions
A.7a,b,e,f
Try It!
State the domain
and range of
the graph
D: -2 < x < 3≤
R: 4 < y < 6