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:
x / 2 / 5 / 9 / 2y / 1 / 4 / 7 / 3
{(2,1), (4,3), (5,4), (9,7)}
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 ______.
EquationFunction 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:
x / 2 / 5 / 9 / 2y / 1 / 4 / 7 / 3
{(2,1), (4,3), (5,4), (9,7)}
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:
Function Notation
- A function that is written as an equation can also be written in a form called
__function notation______.
EquationFunction 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) = 5xf(x) = 8x f(3) = 5(3) or 5 x 3 f(4) = 8(4) or 8 x 4
f(3) = 15f(4) = 32