Functions

Functions

Relation - A set of ordered pairs

EX: {(2,1), (3,1), (0,4), (2,-1)

• Domain - Set of all x - coordinates - Ex: {0, 2, 3}

• Range - Set of all y - coordinates - Ex: {-1, 1, 4}

• list values in order from smallest to biggest & don't repeat values!

Function:

 A relation in which each element of the domain is paired with exactly one element from the range.

No repeat x-values.

Or use the Vertical Line Test - Shows whether a relation is a function by testing whether a single domain element is mapped to more than one range element (if the line crosses more than one point, it is NOT a function).

Multiple Choice

Is this mapping a function?

• yes

• no

Multiple Choice

Is this mapping a function?

• yes

• no

Multiple Choice

Is this mapping a function?

• yes

• no

Is this a function?

Use the Vertical Line Test...

Domain and Range

on a graph.... domain is all x values and range is all of the y values the graph covers.

Use [ ] for numbers included in your graph.

Use ( ) for number not included in your graph (like +/- 00)

Find domain & range

• Domain: 

   $\left(-\infty,\infty\right)$  

• Range:   $\left(-\infty,\ \infty\right)$  

Find Domain & Range

• Domain: [-3, 00) 

• Range:  $\left(-\infty,\ \infty\right)$  

Multiple Choice

Find the Domain:

• [-2, 00)

• (-00, 00)

• [0, 00)

• (-2, 00)

Multiple Choice

Find the range:

• (-00, 00)

• [-2, 00)

• [0, 00)

• (-2, 00)

Discrete VS Continuous

• Discrete - set of unconnected points

• Continuous - infinite number of elements, graphed with a line or smooth curve