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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: crayolé on April 07, 2010, 07:11:39 pm

Title: Modulus as hybrid functions?
Post by: crayolé on April 07, 2010, 07:11:39 pm: Can someone please explain to me how this works?

I'm having a lot of trouble trying to grasp this concept ( turning a modulus function into a hybrid function)
Title: Re: Modulus as hybrid functions?
Post by: superflya on April 07, 2010, 07:13:00 pm: i suggest u read this http://vcenotes.com/forum/index.php/topic,24739.0.html
Title: Re: Modulus as hybrid functions?
Post by: brightsky on April 07, 2010, 07:15:36 pm: Perhaps it would be more helpful if you posted up a question or two on it. ;)
Title: Re: Modulus as hybrid functions?
Post by: crayolé on April 07, 2010, 07:47:42 pm: Alright,

What would be the steps you would take to write |2x+3| as a hybrid function?
Title: Re: Modulus as hybrid functions?
Post by: superflya on April 07, 2010, 07:56:48 pm: take out the 2, $2|x+\frac{3}{2}|$

split into 2 cases

$2(x+\frac{3}{2}), x\geq \frac{-3}{2}$

$-2(x+\frac{3}{2}), x< \frac{-3}{2}$

theres ur hybrid.
Title: Re: Modulus as hybrid functions?
Post by: Blakhitman on April 07, 2010, 07:59:21 pm: Ok, this is my attempt at explaining it, (I'm stupid but, so let someone confirm :P ).

Take the modulus function $y=\left | 2x + 3 \right |$

We know that the absolute value function only spits out magnitude, so only positive numbers, now this is where the hybrid comes in.

We know that when $2x + 3\geq 0$ then $y= 2x + 3$ . However when $2x +3 < 0$ , then the terms in the modulus must be multiplied by a negative to make it into a positive, so $y= - (2x + 3)$ .

So the hybrid function of this would be:

$y= \begin{Bmatrix} 2x + 3, & 2x + 3 \geq 0 \\ -2x - 3 & 2x + 3 <0 \end{Bmatrix}$

Then you solve for x in the domain, I usually do this before writing the hybrid function.

$y=\begin{Bmatrix} 2x + 3, & x \geq \frac{-3}{2} \\ -2x - 3, & x <\frac{-3}{2} \end{Bmatrix}$

EDIT: Beaten...
Title: Re: Modulus as hybrid functions?
Post by: crayolé on April 07, 2010, 08:50:28 pm: Thanks Blak for the long explanation ;]
I think i get it now