# Function Discovery

Topics: Polynomial, Maxwell's equations, Derivative Pages: 1 (360 words) Published: June 23, 2013
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