Algebra - Introduction to Functions

Introduction to Functions

Algebra 1

Lesson Goals - Understand functional relationships

• SWBAT define a function in terms of its input and output

• SWBAT identify the domain and range of a relation

• SWBAT determine whether or not a function is a relation

Vocab

• Function: a relation in which each element of the domain is mapped to (paired with) exactly one element of the range

• Domain (x): the set of input values for which a function is defined

• Range (y): the set of output values corresponding to the domain values

• Relation: a set of ordered pairs

• Independent Variable: the variable in a function that represents the input values; the first coordinate in an ordered pair - the x value

• Dependent Variable: the variable in a function that represents the output values; the second coordinate in the ordered pair - the y value

Relation or Function?

• All functions are relations, but not all relations are functions.

• A function must have a unique input for every output.

• The domain (x-value) may only be used once.

• The range (y-values) may be used more than once if they have different domains (x-values)

Vertical Line Test

• Visual representation to see if a relation is a function.

• If a vertical line passes through no more than one point, then the graph represents a function.

Multiple Choice

What is the definition of function?

• Has inputs and outputs

• Every input has only ONE output

• Inputs have different outputs every time

• x-values and y-values

Multiple Choice

All of the x values or inputs are called what?

• Domain
• Range
• Relation
• Function

Multiple Choice

All of the y values or outputs are called what?

• Domain
• Range
• Relation
• Function

Multiple Choice

Is this graph a function or not a function? 

• Function 
• Not a Function

Multiple Choice

Which graph does NOT pass the vertical line test?

• Graph 1
• Graph 2
• Graph 3
• Graph 4

Multiple Choice

Which set of values is a function?

• (9,5) (10,5) (9,-5) (10,-5)
• (3,4) (4,-3) (7,4) (3, 8)
• (6,-5) (7, -3) (8, -1) (9, 1)
• (2, -2) (5, 9) (5, -7) (1, 4)

Multiple Choice

Does this relation represent a function?
(1,5), (1,6), (1,7), (1,8), (1,9)

• Yes
• No

Multiple Choice

What is the range of the following relation:
(9, -2) (4, 3)  ( 8, 10) ( -4, 8)

• -4, 4, 8, 9
• -2, 3, 8, 10
• (9, -2) ( 4, 3)
• (8, 10) (-4, 8)

Multiple Choice

Is this graph a function or not a function? 

• Function
• Not a Function 

Multiple Choice

Is this graph a function or not a function? 

• Function
• Not a Function

Multiple Choice

Is this mapping a function or not a function? 

• Function
• Not a Function

Multiple Choice

Is the relation a function? Why.

• Yes, because the x-value 11 has two y-values pair with it.
• Yes, because each x-value has only one y-value paired with it.
• No, because the x-value 11 has two y-values pair with it.
• No, because each x-value has only one y-value paired with it.

Poll

What is your level of understanding of functions right now?

• This is easy, I've got this

• I get it, but may have some questions as I work through the assignments.

• I am confused and need help. I will email you to set up a time.

• What class is this?