warm up. functions defined essential question: how can you determine if a relation is a function?

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Page 1: Warm Up. FUNCTIONS DEFINED Essential Question: How can you determine if a relation is a function?

Warm Up

1) 2)

Page 2: Warm Up. FUNCTIONS DEFINED Essential Question: How can you determine if a relation is a function?

FUNCTIONS DEFINEDEssential Question: How can you determine if a relation is a function?

Page 3: Warm Up. FUNCTIONS DEFINED Essential Question: How can you determine if a relation is a function?

Key Terms

• Function: A relation where for every Input there is exactly

ONE Output.

• Relation: A set or group of Ordered Pairs.

• Domain: The X-values or Input.

• Range: The Y-values or Output.

Page 4: Warm Up. FUNCTIONS DEFINED Essential Question: How can you determine if a relation is a function?

How can you tell if a Relation is a Function?

X Y

1 2

3 5

6 1

• For every X-value there is only 1 Y-value.

• A relation is NOT a function if an X-Value has 2 or more Y-Values.

Domain: Range:

Page 5: Warm Up. FUNCTIONS DEFINED Essential Question: How can you determine if a relation is a function?

NOT a Function

X 1 3 4 6 7 3

Y 2 4 5 7 9 6

Domain: Range:

Page 6: Warm Up. FUNCTIONS DEFINED Essential Question: How can you determine if a relation is a function?

Determining if a Graph is a Function

• A graph is a function if it passes the Vertical Line Test.

• If a vertical line is drawn anywhere on the coordinate plane, it should only touch the “function” once.

Domain: Range:

Page 7: Warm Up. FUNCTIONS DEFINED Essential Question: How can you determine if a relation is a function?

NOT a Function

Domain: Range:

Page 8: Warm Up. FUNCTIONS DEFINED Essential Question: How can you determine if a relation is a function?

Examples for Tickets

Page 9: Warm Up. FUNCTIONS DEFINED Essential Question: How can you determine if a relation is a function?

Function or Not a Function?

X Y

2 -4

3 0

4 5

Page 10: Warm Up. FUNCTIONS DEFINED Essential Question: How can you determine if a relation is a function?

Function or Not a Function?Domain and Range

X Y __

3 4

2 0

1 7

Page 11: Warm Up. FUNCTIONS DEFINED Essential Question: How can you determine if a relation is a function?

Function or Not a Function?

Page 12: Warm Up. FUNCTIONS DEFINED Essential Question: How can you determine if a relation is a function?

Function or Not a Function?Domain and Range

Page 13: Warm Up. FUNCTIONS DEFINED Essential Question: How can you determine if a relation is a function?

Function or Not a Function?