5.2

Relations & Functions

5.2 – Relations & Functions

Evaluating functions Remember, the DOMAIN is the set of

INPUT values and the RANGE is the set of OUTPUT values.

y = 3x + 4

inputoutput

Another way to remember them is…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}

The relation {(2,1), (-1,3), (0,4)} can be shown by either……

1) a table.

2) a mapping.

3) a graph.

x y

2-10

134

2-10

134

Given the following table, show the relation, domain, range, and mapping.

x -1 0 4 7y 3 6 -1 3

Relation = {(-1,3), (0,6), (4,-1), (7,3)}Domain = {-1, 0, 4, 7}Range = {3, 6, -1, 3}

Mappingx -1 0 4 7y 3 6 -1 3

You do not need to write 3 twice in the range!

-1047

36-1

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

Functions

A 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

Function Notation

Output

InputName of Function

y f x

Determine whether each relation is a function.1. {(2, 3), (3, 0), (5, 2), (4, 3)}

YES, every domain is different!

f(x)2 3

f(x)3 0

f(x)5 2

f(x)4 3

Determine whether the relation is a function. 2. {(4, 1), (5, 2), (5, 3), (6, 6), (1, 9)}

f(x)4 1

f(x)5 2

f(x)5 3

f(x)6 6

f(x)1 9

NO, 5 is paired with 2 numbers!

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

5.2 – Relations & Functions

Example: Evaluate the function rule f(a) = -3a + 5 to

find the range of the function for the domain {-3, 1, 4}.

5.2 – Relations & Functions

To solve this, all you have to do is plug ALL of the numbers in for a and solve.

f(a) = -3a + 5

f(-3) = -3(-3) + 5

f(-3) = 9 + 5

f(-3) = 14

5.2 – Relations & Functions

Once you have done this for ALL of the numbers, you would write your answer from smallest to largest like the following: {-7, 2, 14}

5.2 – Relations & Functions

Make a table for f(n) = -2n + 7. Use 1, 2, 3, and 4 as domain values.

2

n f(n)

1

2

3

4