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35 Cards in this Set
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given f(x)=a*b^x
b>1 
exponential growth function


given f(x)=a*b^x
b<1 
exponential decay function


end behavior of decay

lim x>inf. f(x)=0
lim x>inf. f(x)=inf. 

end behavior of growth

lim x>inf. f(x)=inf.
lim x>inf. f(x)=0 

transformations:
f(x)=2^x shift right c 
f(x)=2^(xc)


transformations:
f(x)=2^x reflect across yaxis 
f(x)=2^x


transformations:
f(x)=2^x vertical stretch by c 
f(x)=c*2^x


transformations:
f(x)=2^x reflect across xaxis 
f(x)=2^x


transformations:
f(x)=2^x horizontal shrink of 1/c 
f(x)=2^cx


any exp. function can be written as

f(x)=a*e^kx


given f(x)=a*e^kx
a>0 and k>0 
exp. growth function


given f(x)=a*e^kx
a>0 and k<0 
exp. decay function


Logistic Growth Function

f(x)=c/(1+a*b^x) or f(x)=c/(1+e^x)
if a=c=k=1, then f(x)=1/(1+e^x) 

yint. of f(x)=c/(1+a*b^x)

f(0)


log[b]1=

0


log[b]b=

1


log[b]b^y=

y


b^(log[b]x)=

x


log[10]x=

logx


log[e]x=

lnx


ln1=

0


lne=

1


lne^y=

y


e^(lnx)=

x


transformations:
f(x)=lnx shift right c 
f(x)=ln(xc)


transformations:
f(x)=lnx reflect over yaxis 
f(x)=lnx


transformations:
f(x)=lnx reflect over xaxis 
f(x)=lnx


transformations:
f(x)=lnx vertical stretch of c 
f(x)=c*lnx


transformations:
f(x)=lnx shift up c 
f(x)=lnx+1


Product Rule

log[b](RS)=log[b]R + log[b]S


Quotient Rule

log[b](R/S)=log[b]R  log[b]S


Power Rule

log[b]R^c=clog[b]R


Change of Base

y=log[4]7
1)Change to exp. form: 4^y=7 2)Apply ln or log[10]: ln4^y=ln7 3)Power Rule: yln4=ln7 4)Divide: y=(ln7)/(ln4) 

g(x)=lnx/lnb=(1/lnb)*lnx
if b>1 
vertical stretch or shrink by 1/lnb


g(x)=lnx/lnb=(1/lnb)*lnx
if 0<b<1 
reflection over xaxis
