topics 2 :
Functions
,⑦ Functions review Parti :
⑦ linear
functions . -
4
⑦ y -
-
mxtc -3 "*
⑦
grad y step
-
increased decreases at a constant rate (m ) .
-
z
x step
⑦ it
-
is graphed as a straight line .
-
i
•
⑦ y intercept
the
-
mis
gradient .
-
l
l
l l l '
l 2 3 4
⑦ cis
they intercept -
.
- -
i
⑦ Quadratic functions : y
⑦ n
all 0
When graphed they make ,
a parabolic shape .
⑦
They increase decrease at an
increasing rate .
⑦
y
-
-
ax2tbxtC=O x
⑦ axis
of symmetry :
X -
-
IT -
-
X coordinate of vertex
-
.
Y
⑦ BITE BIT
quadratic formula -
-
-
=
-
,
att A O
2A 2A
positive quadratic
⑦
Discriminant O :
used to determine how
many x -
intercepts there are .
x
⑦ O 2. roots .
⑦ =D I root t t
.
⑦ O no real roots .
negative quadratic
⑦ domain txt
⑦ ⑦ it
Writing functions notation : is the input .
⑦ ⑦ Y)
flxt danger (
'
'
ex : flxtx -2
⑦ ⑦ it
fix -12-2 is the outcome variables
'
f :x= ex :
.
⑦
y=
'
ex : y=X2 -
2
⑦
Finding a function with a known input Ix ) :
⑦ When and solve
finding f Of some number replace
,
X with this number in the equation .
⑦
Example FIX)=x
'
: -2
, find for x=3
f. 131=135-2 y
" "
f- ( 31=9-2
f. ( 31=7
x
⑦ ⑦
Example of domain and range fix ) : -
-
X -2
'
Domain ( DKXEIR •
-
z
⑦
*
identify it is a quadratic .
Range 1121=9 -2
*
positive parabola since a O
, nthltlllrnfllfhcltcffhsn
.
cs Wednesday .tl November
T
y
⑦
Example Iof domain and range :gtxt=xt3 • 3
⑦
*
identify it is linear Domain ( DKXEIR
x
.
⑦
*
positive m , thus
increasing .
Range ( RKYEIR ,
y
⑦
Example 3 of domain and range.mx/=TxtI
i
,
⑦
*
identify it is an exponential .
Domain (D) =Xz -
I
• x
I
⑦
-
*
( + 1) →
shift 1 unit to the left from O .
Range 1121=970
⑦
Composite functions :
⑦
Function of a function .
⑦ To
operate replace input
,
variable of function 1. with equation of function 2 .
⑦
Notation :
fogtxllgoffx) * most common .
⑦ ⑦
Example 't fog (x) :
where flx) 212-2 and gtx )=xt3
-
-
Example 2 goftx) : where
gtx) -_xt3 and flxtx
'
-2
f. ( x)=XZ -
2 91×1=21+3
f. ( Xt 3) ( Xt 312 gtx -21=1×2-21+3
'
= -
2
fog (X ) X 't 2×+9-2 goflx )=XZ 21-3
-
-
-
( x ) -_x2t2Xt7 X't I
fog g. of ( x )
-
-
⑦ Inverse functions it is the reflection of the original function
:
.
⑦ '
Notation :
f- (x )
⑦
Question
'
type :
find f- Ix ) .
⑦
Solving steps : 1. write equation equal toy .
2. swap x and y .
3. make y the subject .
⑦ Example find f- ( x )
'
' ⑦ Example 2: (x ) for
find
'
1 for flxtx -2 h hlx ) Txt
-
:
§
-
-
y "
y=x2 -2 y Txt -_
x-p -2 *
yrs
Xt2=yZ X2=yt1
Txt's x' t
y y
-
-
-
'
f- ( x ) Txt
' '
h 1×1=212-1
-
-_
Functions
,⑦ Functions review Parti :
⑦ linear
functions . -
4
⑦ y -
-
mxtc -3 "*
⑦
grad y step
-
increased decreases at a constant rate (m ) .
-
z
x step
⑦ it
-
is graphed as a straight line .
-
i
•
⑦ y intercept
the
-
mis
gradient .
-
l
l
l l l '
l 2 3 4
⑦ cis
they intercept -
.
- -
i
⑦ Quadratic functions : y
⑦ n
all 0
When graphed they make ,
a parabolic shape .
⑦
They increase decrease at an
increasing rate .
⑦
y
-
-
ax2tbxtC=O x
⑦ axis
of symmetry :
X -
-
IT -
-
X coordinate of vertex
-
.
Y
⑦ BITE BIT
quadratic formula -
-
-
=
-
,
att A O
2A 2A
positive quadratic
⑦
Discriminant O :
used to determine how
many x -
intercepts there are .
x
⑦ O 2. roots .
⑦ =D I root t t
.
⑦ O no real roots .
negative quadratic
⑦ domain txt
⑦ ⑦ it
Writing functions notation : is the input .
⑦ ⑦ Y)
flxt danger (
'
'
ex : flxtx -2
⑦ ⑦ it
fix -12-2 is the outcome variables
'
f :x= ex :
.
⑦
y=
'
ex : y=X2 -
2
⑦
Finding a function with a known input Ix ) :
⑦ When and solve
finding f Of some number replace
,
X with this number in the equation .
⑦
Example FIX)=x
'
: -2
, find for x=3
f. 131=135-2 y
" "
f- ( 31=9-2
f. ( 31=7
x
⑦ ⑦
Example of domain and range fix ) : -
-
X -2
'
Domain ( DKXEIR •
-
z
⑦
*
identify it is a quadratic .
Range 1121=9 -2
*
positive parabola since a O
, nthltlllrnfllfhcltcffhsn
.
cs Wednesday .tl November
T
y
⑦
Example Iof domain and range :gtxt=xt3 • 3
⑦
*
identify it is linear Domain ( DKXEIR
x
.
⑦
*
positive m , thus
increasing .
Range ( RKYEIR ,
y
⑦
Example 3 of domain and range.mx/=TxtI
i
,
⑦
*
identify it is an exponential .
Domain (D) =Xz -
I
• x
I
⑦
-
*
( + 1) →
shift 1 unit to the left from O .
Range 1121=970
⑦
Composite functions :
⑦
Function of a function .
⑦ To
operate replace input
,
variable of function 1. with equation of function 2 .
⑦
Notation :
fogtxllgoffx) * most common .
⑦ ⑦
Example 't fog (x) :
where flx) 212-2 and gtx )=xt3
-
-
Example 2 goftx) : where
gtx) -_xt3 and flxtx
'
-2
f. ( x)=XZ -
2 91×1=21+3
f. ( Xt 3) ( Xt 312 gtx -21=1×2-21+3
'
= -
2
fog (X ) X 't 2×+9-2 goflx )=XZ 21-3
-
-
-
( x ) -_x2t2Xt7 X't I
fog g. of ( x )
-
-
⑦ Inverse functions it is the reflection of the original function
:
.
⑦ '
Notation :
f- (x )
⑦
Question
'
type :
find f- Ix ) .
⑦
Solving steps : 1. write equation equal toy .
2. swap x and y .
3. make y the subject .
⑦ Example find f- ( x )
'
' ⑦ Example 2: (x ) for
find
'
1 for flxtx -2 h hlx ) Txt
-
:
§
-
-
y "
y=x2 -2 y Txt -_
x-p -2 *
yrs
Xt2=yZ X2=yt1
Txt's x' t
y y
-
-
-
'
f- ( x ) Txt
' '
h 1×1=212-1
-
-_
