Symmetrie
AchsenSymmetrie zur
y-Achse
:
ftx ) -
FH)
punktsymmetrie zum
Ursprung ftx)
: = -
flx )
Exponentialfunktionen
"
Verlauf fcx ) e
Koeffizienten fan) aeb "
c)
d Asymptoten f- Näherungsgeraden)
-
:
in
-
: -_ +
y
µm
"
b
Ansteigendes / fallendes Verschiebung in Richtung FH ) e
Asymptote 5- 0
-
:
c ×
-
: -
" '"
Schaubild
( < o : nach rechts ✗
"° " ) FLX) - +2
•
×
b > O:
ansteigendes Schaubild c > o :
nach links
Asymptote y=2
BLO : fallendes -
" -
✗
flx) -
_
e- + ✗ -
I
Asymptote 5- ✗ -
I
Spiegelungen a. eb
" -
c)
+ d
ei ×
waagr Asymptote
:
e-
.
in → parallel zur x-Achse ; Bsp y=5
a
Streckung Stauchung / d:
Verschiebung y Richtung
.
: -
ex e-
×
in
y Richtung y=d ist die Asymptote senkr
Asymptote
-
- -
:
.
a > | :
„ Seiler
" d >O :
nach Oben → parallel zur y-Achse ; Bsp y=✗
0 >
☐ < „„ flacher
"
do :
nach unten
schiefe Asymptote :
O : ander x-Achse
gespiegelt
<
☐
→ schief
Funktionen
Trigonometrische
Verlauf Koeffizienten Beispiel Sink )
y
sink)
a. Amplitude c :
Verschiebung in × -
Richtung
Abstand zur Mittellinie < < O :
nach rechts
'° " "
"
C > o nach links
Streckung y Richtung
:
„
in -
fix ) = a. sinlblx c) + d -
b:
Periodenlängen
d :
Verschiebung in
y
-
Richtung
" Dauer eines Durchlaufes
"
„ Höhe der Mittellinie "
Streckung in × -
Richtung um b d >o :
nach oben
dco :
nach unten
P 21T
D= Y =
a=
Ymaxtymin
2
< >
p = 21T
Umkehr funktion -
Zeichner
Rechnerische
Bestimmung .
Bestimmung
1) vertauschen von ✗ und
y
:
y
-
-2×+2 ✗ =
Zytz Spiegelung an der I. Winkel hausierenden (y )
'
2) Auf / ÖS .
nach
y
:
✗ =
Zy +2
y =
0,5×-1 f- (x ) -
0,5×-1
T =L
'
D= ] W ]
-
=
. .
; . . .
. . .
; . . .
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