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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^(x-c)
transformations:
f(x)=2^x reflect across y-axis
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 x-axis
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)
y-int. 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(x-c)
transformations:
f(x)=lnx
reflect over y-axis
f(x)=ln-x
transformations:
f(x)=lnx
reflect over x-axis
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 x-axis