# Slide 1 Peelschools org Function Function Notation by wuzhengqin

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• pg 1
Function    Function Notation       Function Formula

y  x2     y  f [3( x  7)]  8   y  [3x  7 ]2  8
1                                         2
y         y  4 f [2( x  1)]        y
x                                       x 1

y     x      y  5 f ( x)  7        y 5 x 7

y  3x        y  f ( 2 x)  8         y  6x  8
1.4 – Domain & Range
Domain:                         Range:
- the x-values of a relation    - the y-values of a relation

Determine the domain and range of
the relations on the following pages.
Using set notation.
Two methods of expressing
domain and range
1. Set Notation
2. Interval Notation
What is set notation?

Set Notation:
A set is merely a collection of elements or
members. So in math it is a collection of
numbers.
Set notation is like a special language that
we use to express what domain and range
is covered by a function.
What is interval notation

Interval notation is another way of defining
domain and range… but it is more
efficient!
Open Parentheses ( )
If the value is not included or undefined.
(i.e. holes, asymptotes, or a jump)
Closed Parentheses [ ]
If the value is part of the graph.
Interval Notation
Infinities      or
If the graph continues forever to the right or upwards,
it approaches infinity.
If the graph continues forever to the left or
downwards, it approaches negative infinity.
Union Sign
If there is a break in the graph, join the interval up to
and after that break with the union sign.

BUT, interval notation cannot be used for
discrete functions!
Set Notation

‘x’ belongs to
the set of real
numbers

Domain = {xR}   Range = {yR}
Interval Notation

Domain : x(,)
Range : y(,)
Set Notation

‘y’ is less than
or equal to 6

Domain = {xR}   Range = {yRy6}
Interval Notation

Domain : [

Domain : x(,)
Range : y(,6]
Set Notation

{(2,4), (3,5), (4,6), (5,7)}

Domain = {2,3,4,5}        Range = {4,5,6,7}
OR                         OR

Domain : {x I 2  x  5}       Range: {y I 4  y  7}
Interval Notation

{(2,4), (3,5), (4,6), (5,7)}

Can’t use interval
notation for integers!
Set Notation, because
integers

3
4                  -3
5                   5

D: {3, 4, 5}
R: {-3,5}
Set Notation

‘x’ is greater
than -3, but
less than or
equal to 5

D:{xεR | -3<x≤5}   R:{yεR | y=3}
Interval Notation

D:
R:
Set Notation

Domain = {xR-4x4}   Range = {yR -4y4}
Interval Notation

Domain : x [ 4,4]
Range : y [ 4,4]
‘x’ belongs to
the set of
integers

Domain = {x-6x3}   Range = {y -1y8}
Set Notation

Asympotote
Where the graph
approaches the line but
never actually touches it.
Interval Notation?

D:
R:
f ( x)  3 x  5
This is a linear function (not and not
a)                           vertical or horizontal), so x and y
can be any value.

Domain = {xR}          Range = {yR}

b)   g ( x)  2( x  1)  8
2
• This is a quadratic function.
• It opens upward, thus has a min.
• The min. value is -8.

Domain = {xR}          Range = {yRy-8}
c)   h( x )      x9                         Are there any restrictions
that must be placed on ‘x’,
or will any ‘x’ value work
Can’t be -’ve                  in this function?

So, what values of ‘x’ will not make the
part under the squareroot sign negative?

Domain = {xRx-9}                   Range = {yRy0}
D:X ε [-9,+∞)                         R: Yε [0,+∞)

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