Name: _____________________________________ Date: ________________ Block: _____
Functions
New Vocab
Algebra I – A.7: The student will investigate and analyze function families and
their characteristics both algebraically and graphically, including
a) determining whether a relation is a function;
b) domain and range
Relation – any pairing of a set of ____________ with a set of _____________. We will be
talking a lot about relations as a group of __________________________.
Function – a special kind of ______________ where each ______________ is paired with
one and ONLY one ______________.
Domain – the set of ______ ______ values (in an ordered pair, it is the _______________)
Range – the set of _____________ values (in an ordered pair, it is the _______________)
Independent Variable – the ____________ variable
Dependent Variable – the _____________ variable
Domain vs.
Range
Identify the domain and range of the functions:
1.
Input (x)
Output (y)
0
5
D: {
R: {
1
2
2
2
4
1
}
}
2. { (3, 1); (0, 2); (7, 2) }
D: {
R: {
}
}
Domain vs.
Range
Identify the domain and range of the functions:
3.
D: {
R: {
4.
D: {
R: {
}
}
5.
D: {
R: {
}
}
0
4
2
5
Examples of
relations and
functions
2
3
Relations and functions can be represented in a few different ways:
Let’s represent the following relation: { (-3, 2); (0, 5); (2, 4); (-1, 9) }
Tables
x
Difference
between a
function and
a relation
}
}
Mapping
Graph
y
Every _____________________ is a ____________________ ,
but not every ___________________ is a _____________________.
The only way a relation is a function is that if for every input, _______________________
___________________________________.
Determine if
the relation
is a function
1.
Function
5
2
3
-
Examples:
3
6
or
Not a function
Why? _______________________________
____________________________________
1
Domain:
Range:
2.
Function
or
Not a function
Why? _______________________________
____________________________________
Domain:
Range:
3.
{ (-3, 2); (0, 5); (2, 4); (-1, 9) }
Function
or
Not a function
Why? ______________________________
____________________________________
Domain:
Range:
The Vertical
Line Test
An easy way to tell if graphs are functions is by using the _____________________.
A relation on a graph is a ____________ if no vertical line
passes through ______________________ on the graph.
Examples of
the Vertical
Line Test
Use the Vertical Line Test to determine whether each relation is a function:
Independent
and
Dependent
Variables
1. You are buying concert tickets that cost $15 each. If you buy 6 tickets, how much
will it cost? Identify the independent and dependent variable.
2. Every 30 minutes that you exercise, you burn 200 calories. If you burned 1000
calories, how many minutes have you exercised? Identify the independent and
dependent variable.
3. If you are traveling in a car at 50 miles per hour, and you are driving for 3 hours,
how much distance have you traveled? Identify the independent and
dependent variable.
Practice
ON A PIECE OF SCRATCH PAPER-- Use the following to:
a) Determine whether the following are functions or just relations
b) Find the domain and range
x
y
-3
0
-2
2
1
2
4
5
6
9
1.
2.
3.
4.
x
-3
2
8
-3
y
1
5
2
0
5. Come up with a situation that
involves an independent and
dependent variable.
Hint: Think of something that has
a cause and effect!