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April 7th, 2014, 07:02 PM   #1
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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 y-axis, but how does one translate the function by the x-axis?
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April 7th, 2014, 07:20 PM   #2
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If you want to translate a function horizontally, then use:

$\displaystyle f(x-a)$

to move the function $a$ units to the right. So, your linew, translated $a$ units to the right, becomes:

$\displaystyle y=m(x-a)+b$

Now, this may seem counter-intuitive...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:

$\displaystyle g(x)=f(x-a)$

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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