Functions & Calculus
, "
function
Thestraightlinearaph
① standardize y mate
-
:
-
and
gradient e→ y int
• m - -
line
ma •
y through the ORIGIN
-
- . . .
•
y
-
- K (where K' is
'
a constant ) . . .
line PARALLEL to the X -
Axis
• n = a number . . . line PARAUEC to the Ye -
Axis
② Intercepts Gradient intercept method
• Dual intercept method •
int )
R (let
)
o if equation in
y Merrigan (form
-
- - - -
int (let o)
y n
y ma
-
-
- - - -
③ Gradients
4h
^
#
a
m
*
• -
-
.
V
If l 1112 then
v
m m> O meo
ma
• -
-
, .
If l Ik then
^ ^
mix me I
# #
• =
,
-
→
Negate and
Reciprocate : 4=22+3 r re
Z undefined
-
M= O mis
-
ME -
= - 2
,
④ ummm
Finding Equations
i) If given the co-ordinates of ANY 2 POINTS
ii) If
given the GRADIENT and ANY OTHER POINT on the
graph
WBAY
.
.
-
Average Gradient between 2 points on a curve
flat
where
of -
sent 9. Determine
and
the
average gradient between the points A and
B ,
n -
-
2 a- 5
respectively .
①① USE FUNCTION NOTATION :
Aug Gradients ffb)-#
.
=
Ffs ) FG )
-
=
2
£ (2) =3 b -
a
-6
f- (5) = 9
,Theparabola-3F.ms/OyStandard
= azitbntc
Form :
•
y int
- - let n -
-
O
n int to let O
y
• -
=
•
T.P. - N cord
-
ne -
b- ; y
-
cord :
y
-
- C -
to
Za 4A
•
TP .
.
is the MAXIMIN value
② Turning point Form :
a Cn
y Pkt of -
-
-
let
k⑧④m*mw
me 0
y int
• -
→
to
:F .
near .
A. as
•
of is the MAXIMIN value
Bg
③ Root Form :
y= a ca M) (n Nz)
fund
-
-
④ length -
-
top function . ( bottom
•
y -
int → let neo
• aint no bet y -
- o
④ Min =
-
Za units
•
IP -
Nitka
④ Man
.
tha units
z -
-
C -
• T.P. is the MAXIMIN value
④ Domain :
Range :
NER a>o -
y z
of
ALOT
y EG
rib
B
.
SLOR Method
hmmmm
-
tbntc
y = An
If a>o If of and b
c=y-intTp
signs
• is • a •
are same then A. as If c > o then
If
,
As
,
a co
to the Left If
they A. as above Z arm 's
→
-
.
are
Opp then , Right .
If CCO then A. as
,
below the a- anis
, Thetlyperbola
① General Form :
Y )
a-a.pt Ca #
=
of o
determines which quadrant the graph lies
'
'
• a in
a > 0 a co
I
A
*
^
9i% 'The eat
'
'
"
Pe agates I.
• "
tf n -
Pp -
Pp
'
to the right
'
units
VIRILE shift
' '
•
Cf causes a
if 9- up
'
SO
'
→
f units
tf of C o →
'
of units down
②
ALY?Plates
"
the
off Asymptote
is vertical
y
= is the theorizes asymptote
③ Domain and Range :
N E R ; r
Ep → Domain
Y ER ; y # of -0
Range
④ Equations of axes of symmetry :
Gradients of the of and l Therefore
ppg symmetry
• anes are tl -
.
. the equations are
y
-
-
tate or
y
-
-
-
atc
h •
The symmetry pass through the point of intersection of
anes of
the asymptotes .
• Substitute this point into the above equation and solve for c .
, "
function
Thestraightlinearaph
① standardize y mate
-
:
-
and
gradient e→ y int
• m - -
line
ma •
y through the ORIGIN
-
- . . .
•
y
-
- K (where K' is
'
a constant ) . . .
line PARALLEL to the X -
Axis
• n = a number . . . line PARAUEC to the Ye -
Axis
② Intercepts Gradient intercept method
• Dual intercept method •
int )
R (let
)
o if equation in
y Merrigan (form
-
- - - -
int (let o)
y n
y ma
-
-
- - - -
③ Gradients
4h
^
#
a
m
*
• -
-
.
V
If l 1112 then
v
m m> O meo
ma
• -
-
, .
If l Ik then
^ ^
mix me I
# #
• =
,
-
→
Negate and
Reciprocate : 4=22+3 r re
Z undefined
-
M= O mis
-
ME -
= - 2
,
④ ummm
Finding Equations
i) If given the co-ordinates of ANY 2 POINTS
ii) If
given the GRADIENT and ANY OTHER POINT on the
graph
WBAY
.
.
-
Average Gradient between 2 points on a curve
flat
where
of -
sent 9. Determine
and
the
average gradient between the points A and
B ,
n -
-
2 a- 5
respectively .
①① USE FUNCTION NOTATION :
Aug Gradients ffb)-#
.
=
Ffs ) FG )
-
=
2
£ (2) =3 b -
a
-6
f- (5) = 9
,Theparabola-3F.ms/OyStandard
= azitbntc
Form :
•
y int
- - let n -
-
O
n int to let O
y
• -
=
•
T.P. - N cord
-
ne -
b- ; y
-
cord :
y
-
- C -
to
Za 4A
•
TP .
.
is the MAXIMIN value
② Turning point Form :
a Cn
y Pkt of -
-
-
let
k⑧④m*mw
me 0
y int
• -
→
to
:F .
near .
A. as
•
of is the MAXIMIN value
Bg
③ Root Form :
y= a ca M) (n Nz)
fund
-
-
④ length -
-
top function . ( bottom
•
y -
int → let neo
• aint no bet y -
- o
④ Min =
-
Za units
•
IP -
Nitka
④ Man
.
tha units
z -
-
C -
• T.P. is the MAXIMIN value
④ Domain :
Range :
NER a>o -
y z
of
ALOT
y EG
rib
B
.
SLOR Method
hmmmm
-
tbntc
y = An
If a>o If of and b
c=y-intTp
signs
• is • a •
are same then A. as If c > o then
If
,
As
,
a co
to the Left If
they A. as above Z arm 's
→
-
.
are
Opp then , Right .
If CCO then A. as
,
below the a- anis
, Thetlyperbola
① General Form :
Y )
a-a.pt Ca #
=
of o
determines which quadrant the graph lies
'
'
• a in
a > 0 a co
I
A
*
^
9i% 'The eat
'
'
"
Pe agates I.
• "
tf n -
Pp -
Pp
'
to the right
'
units
VIRILE shift
' '
•
Cf causes a
if 9- up
'
SO
'
→
f units
tf of C o →
'
of units down
②
ALY?Plates
"
the
off Asymptote
is vertical
y
= is the theorizes asymptote
③ Domain and Range :
N E R ; r
Ep → Domain
Y ER ; y # of -0
Range
④ Equations of axes of symmetry :
Gradients of the of and l Therefore
ppg symmetry
• anes are tl -
.
. the equations are
y
-
-
tate or
y
-
-
-
atc
h •
The symmetry pass through the point of intersection of
anes of
the asymptotes .
• Substitute this point into the above equation and solve for c .
