 My Math Forum Is It Possible To Write This As A Function With One Definition?
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 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 $\displaystyle f(x) = x|x|$? $\displaystyle f(x) = x^{2} \text{sgn}(x)$ works too, though I prefer the former (and the two are, in fact, equivalent). Thanks from EvanJ 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 $dy/dx$. Thanks from EvanJ 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 Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post yablo Computer Science 0 March 21st, 2014 05:45 PM The_Ys_Guy Algebra 3 February 27th, 2014 12:00 PM Fabion Real Analysis 1 November 11th, 2013 11:37 AM vlappis Calculus 1 January 19th, 2013 02:10 PM maplesyrup23 Calculus 0 February 28th, 2009 01:30 PM

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