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October 3rd, 2015, 07:08 AM  #1 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 639 Thanks: 85  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: 20,629 Thanks: 2077 
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. 

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