Class
Meeting #l------------*fhe
Real
Number
Lin_e
trtegers:
...,-4,-3,-2,-1,A,1,2,3,4,-..
Rptio$al:
Any
number
that
can be
represented
by a
ratio
of
two
integers, n'6, *6*ps
b;.O.
Ifratiqnal.: Not rational.
Give
examples.
non-repeating
unending
decimals
Oslering:
A
number
located
to
the right
of another number
is
greater.
Give examples
Symb-ol.s:
a>b reads
"a
greater
than
b".
a
is
to the
right
of
b on the
number line.
a<b reads
"a i$
less
than
b".
a
is
to
the
left
of b on the number
line.
a
>
b reads "a
is
greater
than
or equal
to b'n. The
possibility
of a=b
is
included.
a
<
b
reads "a
is less
than or equal
to b". The
possibility
of
a=b
is
included.
lntervals
on the
x-*xis
Open Interval:
(a;b):{xla<x<b}.
Show
graph
Closed-Interyal:
[a;b]={xla
< x <bJ.
$how
graph
kfiefvals
invplVieglnflnitv:
[a;*),
(a;*),
G*;a],
(-o;a),
or
(-co;o)..Show
graphs.
Functions
-A
function m.ay
be represented
by
(l)
ordered
pairs,
(2)
an equation,
(3)
by a
graph,
(a)
bV a machine,
(5)
by
a
mapping.
(l)
Q.rdered
pairs:
{(x,y).
A
set of ordered
pairs
where there casnot
be ordered
pairs
containing
the same
first
element and
different2e elements.
Give Example.
(2)
An
equation:
)=f(x),
reads
"y
is
a function
of
x".
y
is the
dependent variable
&
x
is
the
indepeadent
variable.
Each x-value
must
give
one & onlv
one
y-value,
The
set
of
x-values
for which the
function
is
defined
is
called
its
4ograin
& the set of
y-values
that
result
is
called
tlte ranse.
Show
example with
t:*2.
(3)
Bv
a
Sraph:
All
graphs
drawn must
satisfy the
vertical line
test.
That
means
that
all
vertical
lines
drawn on
the
Saph
(that
intersect
the
graph)
must intersect
the
curve in
exactly
one
point.
Show
exarnples.
(4)
By
a
function
machine:
Usually
for
instructional purposes
only. For each
inpgt
(domain
value), there is exactly
one output
(range
value)...Show
example.
(5)
By
a mapping:
A mapping
takes
a number
from one
set
A
(pre
image)
to
a
number
in
another
set
B
(image).
Set
A
contains
all numbers in
the
domain ofthe
functiorq however,
the
range is
a sub-set
ofB
(it
could be
all of
B,
but
not necessarily).
Show
example.
