RELATION AND FUNCTION

​RELATIONS

AND

FUNCTIONS

Open Ended

Konek ka Dyan! Find pairs of pictures that are somhow connected with one another. Justify your pairing.

RELATIONS AND FUNCTIONS​

​Relations: a set of ordered pairs

​Domain: the set of x-coordinates

​Range: the set of y-coordinates

​

​Alert! When writing the domain and range, do not repeat values.

​RELATIONS AND FUNCTIONS

• State the Domain:​

​

• ​State the Range:

​RELATIONS AND FUNCTIONS

State the Domain:​ ​ State the Range:

​Let's Practice!

​State the Domain and the Range of the relation given the sets of ordered pair.

Multiple Choice

• D: (0)

  R: (2,4,6,8,10)

• D: (2,4,6,8,10)

  R:(0)

Multiple Choice

• D: (-2,0,2)

  R: (-5,-2,1,4,7)

• D: (-5,-2,1,4,7)

  R: (-2,0,2)

• D: (-5,-2,1,4,7)

  R: (-2,-2,0,2,2)

Open Ended

RELATIONS AND FUNCTIONS​

• Relations can be written or represented in several ways. ​

• ​We have already seen relations as represented as ordered pairs.

​Ordered Pairs

​Represented as Table

​Represented as Table

Represented by Ma​pping Diagram

• Create two ovals ​with the domains on the left and the range on the right.

• ​Connect elements of the domain with the corresponding elements in the range by drawing an arrow.

• ​Elements are repeated.

​Represented as Graph

​Represented as Rule or Equation

​What have you noticed about the relationships of x-coordinates to y-coordinates?

​Represented as Rule or Equation

​

​

​

​​x + y = 6

​Relations can be represented as :

• ​ordered pair

• ​table

• ​mapping diagram

• ​graph

• ​rule or equation

​Functions

• ​A function is a relation in which the members of the domain ( x-values) DO NOT repeat.

• ​For every x-value, there is only one y-value that corresponds to it.

• ​y-value can be repeated

​

​

​Functions

​Do the ordered pair represent a function or just a relation?

​Functions

​Do the ordered pair represent a function or just a relation?

​Answer:

Function, because no x-coordinate is repeated in the domain.

​Functions

​Do the ordered pair represent a function or just a relation?

​Functions

​Do the ordered pair represent a function or just a relation?

​Answer:

Relation, because 3 is repeated in the domain.

​Functions

Does the map represent a function or just a relation?​

​Functions

Answer:

​Relation, because -2 and 0 are not mapped to exactly one element in the range.

​Functions

Does the map represent a function or just a relation?​

​Functions

Answer:

​Function, because the domain is mapped exactly to one element in the range.

​Remember!

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

​If a relation is a function, x-coordinates CANNOT be repeated; y-coordinates CAN be repeated.

​Let's Practice!

​Verifies if a given relation is a function or just a relation.

Multiple Choice

• Function

• Relation

Multiple Choice

• Function

• Relation

Multiple Choice

• Function

• Relation

Multiple Choice

• Function

• Relation

Multiple Choice

• Function

• Relation

Multiple Choice

• Function

• Relation

​Graph of a Function

• To determine if a given relation is a function represented by graph, we ca use the VERTICAL LINE TEST.

• ​If a vertical line is passed over the graph and it intersects the graph in exactly one point, the graph represents a function.

​

​Functions

​Does the graph represent a function or just a relation?

​Functions

​Answer:

​Function, because when the vertical line passed over the graph, it intersects exactly at one point.

​Functions

​Does the graph represent a function or just a relation?

​Functions

​Answer:

​Relation, because when the vertical line passed over the graph, it intersects more than one point.

​Let's Practice!

​Verifies if a given relation is a function or just a relation.

Multiple Choice

• Function

• Relation

Multiple Choice

• Function

• Relation

Multiple Choice

• Function

• Relation

Multiple Choice

• Function

• Relation

Multiple Choice

• Function

• Relation

Multiple Choice

• Function

• Relation

​What does the diagram imply?

Fill in the Blank

All functions are relations but ____________.