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## Modulus (absolute value)

When and why do I make the equation into a hybrid form when dealing with modulus?

Because it is often to deal with the unsmooth nature of a modulus curve as separate curves for various reasons (algebra, calculus, etc.)

It is basically a way to "break it down" back to basics, rather than looking at something scary like |x^2 + 3x - 10|, you can say: oh, it's actually just made up of two different graphs: the positive (x^2 + 3x - 10) and the negative (-x^2 - 3x + 10)

That's much easier to deal with than to try to understand what the |x^2 + 3x - 10| is.

Rather than giving you a list of times when you use hybrid functions on modulus functions (rote learning is evil!), I would encourage you to use what I said as a thought process for when you might try using this tool to break down the problem. Maths is not about following a set recipe. Problem solving can involve poking your head around in different paths until you find one that works.

"If I find 10,000 ways something won't work, I haven't failed. I am not discouraged, because every wrong attempt discarded is another step forward" - Thomas Edison, inventor of the lightbulb

If you're looking at a modulus problem, and you don't know what to do next, why not try to break it down into two simpler functions, and see if you can apply your knowledge on them instead?

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