7-1 Relations and Functions

7-1 Relations and Functions

​Learning Intent:  Students will identify functions from mapping diagrams, lists of ordered pairs, tables, and graphs.

Success Criteria:  I can identify if a relation is a function or not.


MA.8.F.1.1 Given a set of ordered pairs, a table, a graph or mapping diagram, determine whether the relationship is a function. Identify the domain and range of the relation.

​Learn:  Relations and Functions

 A ________________ is any set of ordered pairs.  The __________________, or _________________, of the relation is the set of x-coordinates.  The __________________, or __________________, is the set of y-coordinates.  Relations can be represented as mapping diagrams, lists of ordered pairs, tables, and graphs.

Open Ended

What is the domain of the relation?

What is the range of the relation?

​A _____________________________ is relation that assigns exactly one output value to each input value. Each value in the domain is paired with exactly one value in the range.

​Which of the following are functions:

​A _____________________________ is relation that assigns exactly one output value to each input value. Each value in the domain is paired with exactly one value in the range.

​Which of the following are functions:

​Learn: Identify a function using ordered pairs.

​Learn: Identify a function using ordered pairs.

​None of the x-values repeat. Each input has exactly one output.

​The x-value of 56 repeats so it has more than one output (130 & 128).
Therefore, this is not a function.

Labeling

Label each relation as a function or not a function.

Drag labels to their correct position on the image

Function

Not a Function

Open Ended

What is the domain and range for the set of ordered pairs?

Open Ended

What is the domain and range for the set of ordered pairs?

​Learn: Identify a function using tables.

​Learn: Identify a function using tables.

​This table represents a function because each input has exactly one output.

​Learn: Identify a function using tables.

​Learn: Identify a function using tables.

​This table does not represent a function because both x-values 1 & 3 have more than one output value.

Multiple Choice

Does the relation represent a function or not?

• Function

• Not a Function

Open Ended

What is the domain for the relation?

Open Ended

What is the range for the table?

Multiple Choice

Does the relation represent a function or not?

• Function

• Not a function

Open Ended

What is the domain and range for the set of ordered pairs?

​Learn:  Identify a function using graphs. 

Use the vertical line test to determine if a graph is a function.  A vertical line should only touch the graph in one place if the graph represents a function.  If it touches the graph in more than one place, it is not a function.

​Learn:  Identify a function using graphs. 

Use the vertical line test to determine if a graph is a function.  A vertical line should only touch the graph in one place if the graph represents a function.  If it touches the graph in more than one place, it is not a function.

​This graph passes the vertical line test so it is a function. The vertical line only touches the graph in one place.

​Learn:  Identify a function using graphs. 

Use the vertical line test to determine if a graph is a function.  A vertical line should only touch the graph in one place if the graph represents a function.  If it touches the graph in more than one place, it is not a function.

​Learn:  Identify a function using graphs. 

Use the vertical line test to determine if a graph is a function.  A vertical line should only touch the graph in one place if the graph represents a function.  If it touches the graph in more than one place, it is not a function.

​The graph does not pass the vertical line test. The vertical line touches two points at the same time.

Labeling

Label each relation as a function or not a function.

Drag labels to their correct position on the image

Function

Not a Function

Categorize

Options (20)

Put under Orange

Put under red

Organize these options into the right categories

Function

Not a Function

Orange

Red

Multiple Choice

Find the DOMAIN

• {-5, -2, 1, 4}

• {1, -2, 4, -5}

• {-1, 0, 2, 3}

• {0, -1, 2, 3}

Multiple Choice

Find the RANGE

• {-5, -2, 1, 4}

• {1, -2, 4, -5}

• {-1, 0, 2, 3}

• {0, -1, 2, 3}

Multiple Choice

What is the domain?

• {-4, -1, 0, 2, 7}
• {-5, -4, -1, 0, 1, 2, 4, 7}
• {-5, 0, 1, 2, 4}
• {5}

Multiple Choice

Identify the domain of the following relation:
Remember domain is the "x" values

• -6, 14, 2, 28
• (-6,14), (0,32), (2,38), (4,44)
• -6, 0, 2, 4
• 14, 32, 38, 44

Multiple Choice

What is the range of the mapping?

• {1, 2, 4}

• {0, 1, 2, 3}

• {0, 3}

• {1, 4}

Multiple Choice

What is the range of the table?

• {-4, 0, 1, 3}

• {-2, 0, 2, 3}

• {-4, -2, 0, 1, 2, 3}

• { (0, 0), (2, -4), (3, 3), (-2, 1) }

Multiple Choice

What is the domain?

• {-2, -1, 0, 1, 8}
• {3, 5, 7 , 9, 0}
• {-2, -1, 0, 1, 3, 5, 7, 8, 9}
• {-2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

Multiple Choice

What is the range?

• {-3, -1, 2, 4}
• {0, 4, 7} 
• {0, 4, 4, 7}
• {7, 4, 0}