WARM UP

•Sit in the same seat as yesterday

•1. What is a function?

•2. What is a relation?

•3. Is the following relation a function {(2,3), (4,7), (-2,4), (1,3)}

•4. Map the following points and determine if they are a function (1,2), (-1, 3), (1, 3), (-2, 4)

Relations and Functions

OBJ: How to determine a domain and range given a relation or a

function

FunctionsA function is a relation in which each

element of the domain is paired with exactly one element of the range. Another way of saying it is that there is one and only one output (y) with each input (x).

f(x)x y

Is this relation a function?{(1,3), (2,3), (3,3)}

1. Yes

2. No

Answer Now

Vertical Line Test (pencil test)

If any vertical line passes through more than one point of the graph, then that

relation is not a function.

Are these functions?

FUNCTION! FUNCTION! NOPE!

Vertical Line Test

NO WAY! FUNCTION!

FUNCTION!

NO!

Is this a graph of a function?

1. Yes

2. No

Answer Now

Given f(x) = 3x - 2, find:1) f(3)

2) f(-2)

3(3)-23 7

3(-2)-2-2 -8

= 7

= -8

Given h(z) = z2 - 4z + 9, find h(-3)

(-3)2-4(-3)+9-3 30

9 + 12 + 9

h(-3) = 30

Given g(x) = x2 – 2, find g(4)

Answer Now

1. 2

2. 6

3. 14

4. 18

Given f(x) = 2x + 1, find-4[f(3) – f(1)]

Answer Now

1. -40

2. -16

3. -8

4. 4

How about some more definitions? The domain is the

set of 1st coordinates of the ordered pairs.

The range is the

set of 2nd coordinates of the ordered pairs.

A relation is a

set of ordered pairs.

Given the relation {(3,2), (1,6), (-2,0)},

find the domain and range.

Domain = {3, 1, -2}

Range = {2, 6, 0}

What would this be?

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

A bad relationship!! Ha! Ha!

What is the domain of the relation{(2,1), (4,2), (3,3), (4,1)}

1. {2, 3, 4, 4}

2. {1, 2, 3, 1}

3. {2, 3, 4}

4. {1, 2, 3}

5. {1, 2, 3, 4}

Answer Now

What is the range of the relation{(2,1), (4,2), (3,3), (4,1)}

1. {2, 3, 4, 4}

2. {1, 2, 3, 1}

3. {2, 3, 4}

4. {1, 2, 3}

5. {1, 2, 3, 4}

Answer Now

Inverse of a Relation: For every ordered pair (x,y) there must be a (y,x).

Write the relation and the inverse.

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

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

-134

-6-42

Write the inverse of the mapping.

-3

43-12

1. {(4,-3),(2,-3),(3,-3),(-1,-3)}

2. {(-3,4),(-3,3),(-3,-1),(-3,2)}

3. {-3}

4. {-1, 2, 3, 4} Answer Now

Let’s review tables!Graph y = 2x + 1 using the domain {0, 1,

4}

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32

1. Make sure the equation is solved for y.

2. Create a t-table using the domain values.

3. Plug in the domain values and solve for the range.

4. Plot the points and connect them to create the line.

x y=2x+1 y

0

1

4

Let’s use the domain {0, 1, 2} for our equation.

2 3y x

Create a t-table by picking at least three numbers to plug into our equation.

x

0 1 2

ordered pairy2 3y x

-2(0) + 3 3 (0, 3)

-2(1) + 3 1 (1, 1)

-2(2) + 3 -1 (2, -1)