
PreCalculus PreCalculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
October 3rd, 2015, 07:08 AM  #1 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 664 Thanks: 87  Is It Possible To Write This As A Function With One Definition?
Take this function where x and y will both be negative, both be 0, or both be positive: If x < 0, y = $\displaystyle x^2$ If x > or = 0, y = $\displaystyle x^2$ Is it possible to write this function with one definition rather than breaking it into two parts? 
October 3rd, 2015, 09:07 AM  #2 
Member Joined: Sep 2015 From: London Posts: 31 Thanks: 6 
How about $\displaystyle f(x) = xx$? $\displaystyle f(x) = x^{2} \text{sgn}(x)$ works too, though I prefer the former (and the two are, in fact, equivalent). Last edited by LearnMathsFree; October 3rd, 2015 at 09:11 AM. 
October 3rd, 2015, 11:17 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,969 Thanks: 2222 
Or $y = x\sqrt{x^2}$, a form that's convenient if you wish to find $dy/dx$.

October 6th, 2015, 01:28 PM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
Or use the "Heaviside step function", $H(x)$ which is defined as 0 if $x< 0$, 1 if $x\ge 0$. Your function is $f(x)= x^2+ H(x)(2x^2)= x^2(2H(x) 1)$.
Last edited by skipjack; October 6th, 2015 at 03:13 PM. Reason: to insert missing 2. 

Tags 
definition, function, write 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Write the output of the neuron as a function of the input  yablo  Computer Science  0  March 21st, 2014 05:45 PM 
Write a simpler function?  The_Ys_Guy  Algebra  3  February 27th, 2014 12:00 PM 
Using compact support to write function as integral  Fabion  Real Analysis  1  November 11th, 2013 11:37 AM 
Write a function in Maple! Question.  vlappis  Calculus  1  January 19th, 2013 02:10 PM 
Write a function notation using y=f(x) as a parent function?  maplesyrup23  Calculus  0  February 28th, 2009 01:30 PM 