# Function Discovery

The plot that shows your data as linear Linear y=mx + Linear Standard graph b Y vs. X Exponential X y=bemx ln(y) =mx+ln(b) Y = mx+B semilogy mx y=b10 log(y) =mx+log(b) log(Y) vs. X Logarithmic* x=bemy ln(x) =my+ln(b) X = my+B semilogx my x=b10 log(x) =my+log(b) Y vs. log(X) Power y=bxm ln(y)=m*ln(x)+ln(b) Y = mX+B log-log log(Y) vs. log(X) *logarithmic equations with calculations done in Excel or MATLAB you will have to solve for x xor you can enter y as independent variable and log(x) as depended variable Transform data into linear form and back Linear Exponential X Do nothing you To linear form already have the 1. y=bemx linear form 2. ln(y) = ln(bemx) 3. ln(y) = ln(bemx) 4. ln(y) = mx+ln(b) 5. Y= mx+B Back to general form 1. Y = mx+B 2. ln(y) = mx+ln(b) 3. eln(y) = e(mx+ln(b)) 4. y = bemx

Linear form

Linear form with variable substitution Linear

Logarithmic To linear form 1. x=bemy 2. ln(x) = ln(bemy) 3. ln(x) = ln(bemy) 4. ln(x) = my+ln(b) 5. X=my+B Back to general form 1. X=my+B 2. ln(x) = my+ln(b) 3. eln(x) = e(my+ln(b)) 4. x = bemy

Power To linear form 1. y=bxm 2. ln(y)=ln(bxm) 3. ln(y)=ln(b)+ln(xm) 4. ln(y)=ln(b)+m*ln(x) 5. Y=mX+B Back to general form 1. Y=mX+B 2. ln(y)=ln(b)+m*ln(x) 3. ln(y)=ln(b)+ln(xm) 4. e(ln(y))=e(ln(b))+e(ln(x^m)) 5. y= e(ln(b)*ln(x^m)) 6. y= b* xm

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