Download Algebra 1

1.6 & 1.7: Functions Notes
Algebra 1
Name ____________________
Date ____________ Block ___
A function is a relationship between numbers. It’s usually written as an equation and
consists of:


a set of INPUTS (we call this set the _____________________) and
a set of OUTPUTS (we call this set the ___________________)
A function pairs each input (x) with EXACTLY one output (y)!
Domain = Input = Independent Variable = x-values
Range = Output = Dependent Variable = y-values
We can display a function in three ways:
1. _______________
Input
(x)
0
Output
(y)
1
1
2
2
2
4
1
2. __________________
1
0
2
1
3
4
2
3. ________________
How to Identify a Function
Remember: a function is a relationship between input and output values where each
input is paired with exactly one output.
The easiest way to determine a function: X cannot repeat! (y can)
Functions
- each x is paired with exactly one y (x doesn’t repeat)
x
Y
1
3
0
2
-1
1
-2
0
0
1
2
{(2, 4), (3, 5), (4, 6)}
1
3
4
2
NOT FUNCTIONS
x
Y
6
3
3
1
0
2
3
4
6
4
3
12
{(3, 5), (4, 7), (4, 8)}
2
18
3 is paired with
two outputs
1
12 is paired with
two outputs
4 is paired with
two outputs
Tell whether the pairing is a function.
1.
2.
3.
x
y
5
2
2
6
5
2
4
4
7
5
3
6
3
8
5
4
8
x
y
3
x
y
8
5
6
3
9
12
__________
__________
__________
The Vertical Line Test
The Vertical Line Test is a quick way to help you determine if a relation is a function.
If all possible vertical lines cross the graph once or not at all, then the graph represents a
function.
The graph does not represent a function if you can draw even one vertical line that crosses
the graph two or more times.
PRACTICE
Study each relation and tell whether it is a function or not. Circle Yes or NO. Tell why.
1.
YES or NO
______________
2.
YES or NO
_____
3.
YES or NO
_____
4.
YES or NO
________
5. {(3, 1), (5, 2), (7, 3)}
YES or NO
_____ _____
6. {(2, 1), (3, 1), (4, 2), (5, 2)}
YES or NO
_____
7.
YES or NO
8.
YES or NO
Making a Table for a Function
To make a table for a function, simply plug in each value of the domain (x) into the
function to get the range (y values).
Ex. 1
y=x+1
domain: 1, 2, 3, 4
Ex. 2
y = 2x
domain: 0, 1, 3, 4
Representing Functions as a Graph
We can represent a function as a graph.
Simply make an x-y table.
Each corresponding pair of input and output values forms an ordered pair we can plot.
y=x+1
y = 2x
20.