Page 68 - Math SL HB Sem 1

FIINCTIONS, EQUATIONS, INIIQUALITIES

7.'THE I],XPONIIN'I'IAL I.'IJNCTION

I)cfinition

[,et a be a positive real number other than l.Thc lunction
(x) a'
"f =
is the exponential fLrnction with base a .
Graphs with a>l

x t-s a' ,x e R ,),
e.s. f(x)=2'

P erties
Domain ,,R=f -,-[
Range : R. = ]0,
"o[
Asymptote : /-0 (orx -axis)
Intercepts : Cuts y-axis at ]0,1[ (o,t)
Other : Increases Igrowthl . ->-.\-
Continuous

('l'he exponential function with base e ,r 2.71828. . . is known as the natural exponential hrnction
and can writc as f(x) - e')

Graphs with 0<a<l
x.-+a',xeR ),

e.g. (x) - I
"f
2

Properties
Domain : x=f-,-[
Range : n- = ]0,-[
((),1
Asymptote : ]-0 (orx-axis) )
lntercepts : Cuts y-axis at ]0,1 [
Other : Decreases Idecayl
Continuous

)\ tl

t2t