Mathematics AA SL IB Diploma Program - Topic 2: Functions
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Module
Math AA SL
Institution
Book
Oxford IB Diploma Programme: IB Mathematics: Analysis and Approaches, Standard Level, Print and Enhanced Online Course Book Pack
Includes detailed notes to the mathematics analysis and approaches course of the IB diploma program course. Worked examples are incorporated into the explanations and IB-style questions.
Summary Oxford IB Diploma Programme: IB Mathematics: Analysis and Approaches, Standard Level, Print and Enhanced Online Course Book Pack - International Baccalaureate (IB)
Internal Assessment IB Diploma Mathematics A&A SL: Relationship between Different Cinematographical Factors and a Film's Opening Weekend Revenue
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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
-
-_
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