Download Function Guided Notes

Relations & Functions—NOTES
Objectives:
 I can identify a function from a written description, table, graph, rule, set of ordered pairs, and/or mapping.
Vocabulary
 Relation: A set of ____________________________.
 Function: A relation in which each member of the _____________ is paired with exactly one member of the
_________________.
 Domain: The set of ______________ values.
 Range: The set of __________________ values.
 Independent Variable: These values are chosen and do not depend on the other variable. In a set of ordered pairs,
the ____________________ is the independent variable.
 Dependent Variable: This value depends on the input value/independent variable because it changes when the
input value changes. In a set of ordered pairs, the ___________________ is the dependent variable.
Key Concepts
Determining if a Relation is a Function

A relation is a function if each ____________________ is matched up with ONLY ONE
_____________________.

To determine from a list or table.

Does a number in the domain match up with two different numbers in the range?

No—Then the set of ordered pairs is a function.

Yes—Then the set of ordered pairs is not a function because one x-value has two
different y-values.
Examples:
{(2,1), (4,3), (5,4), (9,7)}
x
2
5
9
2
y
1
4
7
3
Determining if a Relation is a Function from a Graph

To determine if a relation is a function when the ordered pairs have been graphed, you can apply the
_________________________________________ to the graph of the relation.

Place a pencil at the left of the graph along the _______________________.

If, for each value of x in the domain, the pencil passes through only one point of the graph, then
the graph represents a function.
Example:
Function Notation
 A function that is written as an equation can also be written in a form called
_______________________________________.

Equation
Function Notation
y=4x
f(x) = 4x
The number in the ( ) will tell you what to sub for x in the problem.
Examples:
Find f(3) if f(x) = 5x.
Find f(4) if f(x) = 8x
Relations & Functions—NOTES
Objectives:
 I can identify a function from a written description, table, graph, rule, set of ordered pairs, and/or mapping.
Vocabulary
 Relation: A set of ____ordered pairs________________________.
 Function: A relation in which each member of the __x-coordinate______ is paired with exactly one member of the
_y-coordinate__________.
 Domain: The set of ____x___ values.
 Range: The set of _________y_________ values.
 Independent Variable: These values are chosen and do not depend on the other variable. In a set of ordered pairs,
the ____x-coordinate_______ is the independent variable.
 Dependent Variable: This value depends on the input value/independent variable because it changes when the
input value changes. In a set of ordered pairs, the _____ y-coordinate _________ is the dependent variable.
Key Concepts
Determining if a Relation is a Function

A relation is a function if each ___ x-coordinate _________ is matched up with ONLY ONE
____________y-coordinate _______________.

To determine from a list or table.

Does a number in the domain match up with two different numbers in the range?

No—Then the set of ordered pairs is a function.

Yes—Then the set of ordered pairs is not a function because one x-value has two
different y-values.
Examples:
{(2,1), (4,3), (5,4), (9,7)}
Because there is
only one yvalue for every
x-value, this IS
a function!
x
y
x
2
5
9
2
x
y
2
1
y
1
4
7
3
2
1
4
3
5
4
5
4
9
9
7
7
3
Because the xvalue of 2 has yvalues of both 1
and 3, this IS
NOT a function!
Determining if a Relation is a Function from a Graph

To determine if a relation is a function when the ordered pairs have been graphed, you can apply the
_________pencil line test____________ to the graph of the relation.

Place a pencil at the left of the graph along the __x-axis___________.

If, for each value of x in the domain, the pencil passes through only one point of the graph, then
the graph represents a function.
Example:
This graph does represent a
function because the pencil
does not touch two points
at the same time as you roll
it along the x-axis.
Function Notation
 A function that is written as an equation can also be written in a form called
__function notation______.

Equation
Function Notation
y=4x
f(x) = 4x
read as F of X
The number in the ( ) will tell you what to sub for x in the problem.
Examples:
Find f(3) if f(x) = 5x.
Find f(4) if f(x) = 8x
f(x) = 5x
f(3) = 5(3) or 5 x 3
f(3) = 15
f(x) = 8x
f(4) = 8(4) or 8 x 4
f(4) = 32