We saw yesterday that every relationship between x- and y-values represent a relation.

That means every graph on a coordinate grid represents a relation

How can we write thisrelation down?

As ordered pairs,a table, or a mappingdiagram.

{(1,5),(3,5),(4,2),(6,-2)} Is it a function?

How can we writethis relation down?

We cannot write every point on this graph down – there is always another in between so the only way is to write an equation.

y = 2x + 4 Is this a function?

D: {1,3,4,6} R: {-2,2,5}

D: x can be anything

R: y can be anything

A better way is to use set notation

To use the symbols of algebra, we could write the domain as

Rxx :

Does that look like a foreign language?

Let’s translate:

The curly braces

just tell us we have a set of numbers.

The x reminds us

that our set contains x-values.

x

The colon says,

such that

:x

: xx

The symbol that looks like an e

(or a c sticking its tongue out)says, belongs to

or is an element of. . .

And the cursive, or script,

R

R xx:

is short for the set of real numbers.

R, the set

So we read it,

“The set of x

:

such thatx belongs to

x Rx

of real numbers.”

“The set of y, such that

y belongs to R,

the set of real numbers.”

Read this:

Ryy :

the domain and range can be any real number.

It is not always true that

Sometimes mathematicianswant to study a function over

a limited domain.

What do you think of the domain?

What about the range?

}:{ Rxx

}2,:{ yRyy

What do you think of the domain?

What about the range?

Function or not?

}61,:{ xRxx

}61,:{ yRyy

What do you think of the domain?

What about the range?

Function or not?

}51,:{ xRxx

}32,:{ yZyy

HW WorksheetDomain and Range

• When we know that a relation is a function, the “y” in the equation can

be replaced with f(x).• f(x) is simply a notation to designate a function. It is pronounced ‘f’ of ‘x’.

• The ‘f’ names the function, the ‘x’ tells the variable that is being used.

Since the equation y = x - 2 represents a function, we can also write it as f(x) = x - 2.

Find f(4):f(4) = 4 - 2f(4) = 2

If g(s) = 2s + 3, find g(-2).g(-2) = 2(-2) + 3

=-4 + 3 = -1

g(-2) = -1

If h(x) = x2 - x + 7, find h(2c).h(2c) = (2c)2 – (2c) + 7

= 4c2 - 2c + 7

If f(k) = k2 - 3, find f(a - 1) f(a - 1)=(a - 1)2 - 3 (Remember FOIL?!)

=(a-1)(a-1) - 3 = a2 - a - a + 1 - 3 = a2 - 2a - 2

pg 635 #2, 4, 6, 8 (no sketch)

Solve the equation for y.

Substitute any value for x and find how many answers it produces for y.

One: function More than one: not

a function

2x + 4y = 8 y = -0.5x + 2 This equation

produces one output for every input so it is a function

xy

xy

4

16 22

This equation will produce two outputs for every input and is therefore not a function

If and find:

2

1)(

x

xxf xxg 4)(

2

174

2

)2(41

42

1

2

x

xx

x

xxx

xx

x

gf

If and find:

2

1)(

x

xxf xxg 4)(

xx

xxx

x

xx

x

gf

84

14

1

2

1

42

1

/

2

If and find:

2

1)(

x

xxf xxg 4)(

2

174

2

)2(41

42

1

2

x

xx

x

xxx

xx

x

gf

Worksheet

Finding and Graphing