Relations:

A relation is a set of ordered pairs.

Ex: {(5, -6), (-3, 4), (2, 1), (5, 6), (-2, 1)}

The domain is the set of x-coordinates (1st coordinate) of the ordered pairs.

The range is the set of y-coordinates (2nd coordinate) of the ordered pairs.

#’s CANNOT REPEAT when writing answer.

Ex:

Ex:

Relations can be shown three different ways:

1) a table. 2) a mapping.

3) a graph.y

x

Ex 1: Display the relation {(2,1), (-1,3), (0,4), (0,1)} as a table, mapping and graph

x y2-100

1341 2

-10

134

Inverse Relation:

Relation = {(-1,-6), (3,-4), (3,2), (4,2)}Inverse = {(-6,-1), (-4,3), (2,3), (2,4)}

-134

-6-42

For every ordered pair (x,y) there must be a (y,x).

Write the relation and the inverse

Functions: (fxn)• Relations in which each element of the domain is paired with

exactly one element of the range

• all x values must be different (no repeating)

• It doesn’t matter if y values repeat

• Is the following relation a function? {(2,4), (3,9), (4,16), (0,0), (5,25)}

Fxns as graphs:

»Vertical Line Test: If every vertical line intersects the graph of a relation in no more than

ONE point, then the relation represents a function

y

x

Function

y

x

Function

y

x

Not a Function

y

x

Not a function

y

x

Function

y

x

Function

Vertical Line Test

Determine which is not a function:y

x

y

x

y

x

0

-4

5

1

-2

A. B.

C. D.

A

Function notation

f(x)Notation is read: f of x

Names the function Tells what variableis in the function

f(x) replaces “y =” in a functionEx: y = -2x + 3 can be rewritten as f(x) = -2x +3

Write the following in function notation:

• y = 4x – 6 f(x) = 4x - 6• y = 3d – 10 f(d) = 3d - 10• y = -5t2 f(t) = -5t2

Evaluating Functions• HINT: It’s just like SUBSTITUTION

Ex: f (x) = x2 – 12 find f (-5)

f (-5) = (-5)2 – 12

f (-5) = 25 – 12

f(-5) = 13

Evaluating Functions• HINT: It’s just like SUBSTITUTION

Ex: f(x) = x2 – 5x + 7 g(x) = -2x + 10

Find: a.f(-2) b. h(-3) c. g( )2

35

26)(

xxh

F(-2) = (-2)2 – 5(-2) + 7

F(-2) = 4 + 10+ 7

F(-2) = 21

g(3/2) =-2(3/2) + 10

g(3/2) = - 3 + 10

g(3/2) = 7

52)3(6)3(

h

4)3(520

5218)3(

h

h

Given the graph, find the following:

Reading Graphs:

A. f(0) = 3 B. f(-4)= -3 C. f(-2) = 5

D. f(-1) = 0 E. f(1) = -3 F. f(4) = 6

x

y