Function Discovery
Function Discovery Quick Reference Sheet by Maxwell Cohen Table of functions used in ENGR 132 Type of equations General form
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
This and many other helpful resources can be found at http://web.ics.purdue.edu/~cohenm/fye.html
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
This and many other helpful resources can be found at http://web.ics.purdue.edu/~cohenm/fye.html