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April 7th, 2014, 07:02 PM  #1 
Senior Member Joined: Feb 2014 From: Louisiana Posts: 156 Thanks: 6 Math Focus: algebra and the calculus  Linear function
In the equation y = mx + b I know that changing b translates the the equation by the yaxis, but how does one translate the function by the xaxis?

April 7th, 2014, 07:20 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 466 Math Focus: Calculus/ODEs 
If you want to translate a function horizontally, then use: $\displaystyle f(xa)$ to move the function $a$ units to the right. So, your linew, translated $a$ units to the right, becomes: $\displaystyle y=m(xa)+b$ Now, this may seem counterintuitive...you might wonder why do I subtract from $x$ to move the function in a positive direction? Suppose your function has a root at $x=c$, that is: $\displaystyle f(c)=0$ Now, if we move this function $a$ units to the right, then we expect the root to move to $c+a$. Let's call the translated function $g(x)$, and so we require: $\displaystyle g(x)=f(xa)$ We then find the root has moved to the right: $\displaystyle g(c+a)=f((c+a)a)=f(c)=0$ 

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