Page 68 - Math SL HB Sem 1

FUNC'r'IONS, EQUATTONS, lNt QLTALTT|ES

"7.'I'IIE EXPONE,N'tIAI, FUNC'I'ION

I)cfinition

Let a be a positive real number other than l.The function

.f (*) a,
-_
is the exponential function with base a.
Graphs with a>l

x t-+ a' ,x e R .v
e.g. f(x)=2'

Properties
Domain : n=f
"o,*[
Range : R. = lo,".[
Asymptote : /-0 (orx-axis)
Intercepts : Cuts y-axis at ]0,1 [ ({). I )
Other : lncreases [growthl
Continu<lus

('l'he exponential lunction with base e ,- 2.71828. . . is known as the natural exponential function
and can r,vrite as f(x) = s';

Graphs with 0<a<l
.),
x t-s a',xe R

.f -
e.c. (x)
2

Properties
Domain : B=f-,-[
Range : n' = ]0,-[
Asymptote : /=0 (or.r -aris) ((i, r )
lntercepts : Cuts y-axis at l0,l I
Other : Decreases [decayl
Continuous

il

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