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35 Cards in this Set
- Front
- Back
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given f(x)=a*b^x
b>1 |
exponential growth function
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given f(x)=a*b^x
b<1 |
exponential decay function
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end behavior of decay
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lim x->inf. f(x)=0
lim x->-inf. f(x)=inf. |
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end behavior of growth
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lim x->inf. f(x)=inf.
lim x->-inf. f(x)=0 |
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transformations:
f(x)=2^x shift right c |
f(x)=2^(x-c)
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transformations:
f(x)=2^x reflect across y-axis |
f(x)=2^-x
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transformations:
f(x)=2^x vertical stretch by c |
f(x)=c*2^x
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transformations:
f(x)=2^x reflect across x-axis |
f(x)=-2^x
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transformations:
f(x)=2^x horizontal shrink of 1/c |
f(x)=2^cx
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any exp. function can be written as
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f(x)=a*e^kx
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given f(x)=a*e^kx
a>0 and k>0 |
exp. growth function
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given f(x)=a*e^kx
a>0 and k<0 |
exp. decay function
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Logistic Growth Function
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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) |
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y-int. of f(x)=c/(1+a*b^x)
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f(0)
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log[b]1=
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0
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log[b]b=
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1
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log[b]b^y=
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y
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b^(log[b]x)=
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x
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log[10]x=
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logx
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log[e]x=
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lnx
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ln1=
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0
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lne=
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1
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lne^y=
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y
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e^(lnx)=
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x
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transformations:
f(x)=lnx shift right c |
f(x)=ln(x-c)
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transformations:
f(x)=lnx reflect over y-axis |
f(x)=ln-x
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transformations:
f(x)=lnx reflect over x-axis |
f(x)=-lnx
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transformations:
f(x)=lnx vertical stretch of c |
f(x)=c*lnx
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transformations:
f(x)=lnx shift up c |
f(x)=lnx+1
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Product Rule
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log[b](RS)=log[b]R + log[b]S
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Quotient Rule
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log[b](R/S)=log[b]R - log[b]S
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Power Rule
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log[b]R^c=clog[b]R
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Change of Base
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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) |
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g(x)=lnx/lnb=(1/lnb)*lnx
if b>1 |
vertical stretch or shrink by 1/lnb
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g(x)=lnx/lnb=(1/lnb)*lnx
if 0<b<1 |
reflection over x-axis
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