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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