3/17
Lecture22_
-
set
Problem
↳
ax
+
7-
by
due
today
@
5pm
:c
dxtey=f
-
-
quiz
Canvas
Office Hours
or
-
2
Midterm
sections
:
:
Fri
2.8.2.9
lecture notes :
,
by
appointment
Apr 7ᵗʰ
3.1-3.6
,
2/15
@ 1:25pm
Econ 414
in
10 -12
MI6
:
Monday
due
→
,
4.1-4.7
midterm
.
Last
time
&
-
-
definitions
Function
:
A fxn
is
a
notation
that
role
between
the relationship
variable
For
-
the
/ all
can
take
the
function
indef
the values
independent
on
.
in
.
variable
the
,
"
-
These
other
values
are
the
"
the function
of
dependent
they
make
the txn
ex
.
g. G)
=
domain)
that number
assigns to
other valve
single
a
the
valve
every
depends
former
some
the
and
variable
dependent
describes
or
,
variable
up
the
.
of
All
values
the
together
range
of
.
FFF
-
what
Domain :
is
the
?
domain
2×-470
2×24
✗⑦
,
,
ex
.
f(×)
=
✗2-11
is
✗
real
any
tt
Find the range
Range
-
For
what
that
:
f- ( )
:
x
values of
f-
≥ -1
is
✗
=
.
it true
2. f- (x)
(2×5+1
4×2+1
off
(2×1--21-6)
f- (2-1)
=
.
=
=
4×41=2×2+2
-2×32
-2×2
2×2+1=+2
-
I
-
I
2--1=1
E- E
✗
=
±
Fa
2
(5+1)
2×2-12
.
4.3Graphsoffunctions-
graph
plane ( xy
functions
We
plane)
-
)
axis
( vertical
contains
that
and
)
(horizontal
x-axis
Cartesian
a
on
axis
an
y-axis
a
Quadrant
ay
i
<-÷#i×
Quao
iczis)
-2
-
c
:
!
-
.
.
-
b-
-
-
&
-
-
-
-
-
-
-
-
iq-a.gg
1
Quad
a
-
(a. b)
point
the
line
ex
Quad
3
vertical
y=b
at
lies
line
×=a
the intersection
and
the
4
of
horizontal
.
( 2,3)
.
↑
an
-
ordered pair
Any fxn
represented
of
in
one
our
G. 4)
variable
2- ☐
can
be
Cartesian
plane
.
-
The
set
✗
ex
.
of
graph
is
consider
an
the
f
function
ordered
all
of
a
element
pairs
of
fxn : fcx)
^
the
(× ,f( ))
the
:
is
×
where
domain
off
.
+2×1-2
Y
::¥÷É:%÷¥×
←
consider
g. G)
: E%
¥
.
=
F-
-2
ay
of
fxn
Common
variable
single
.
×
4=-1
y
"
=
"
"
¥
"
"
"
§
I
-
For
-
graphing purposes
The
It's
symbol
T
only
when
values
that
of
we
,
×
do
,
or
assume
we
"
×
solving
that
,
positive
suggests
could
&
.
positive
equation
an
positive
a
roots
solve
negative
root
.
all
for
the equation
roots
.
ex
-
Find
f-
.
(2) ,f( )
0
↓
y=f(x)=
when
-1=26
,
f-
(6)
f(z)=5
flo> =3
f(6) =-3
,
•
☆
B-
.