A request for the Maths gurus here.

[dehaitest]

Would someone like to give a few questions for me to do, relating to modulus functions and trig functions?
For example questions like (from another thread):
"Also definitely practice your absolute values, there can be some tricky graphs in exam 1 which involve them. e.g. Sketch y = \frac{-6}{|2x+3|}. Sketch y = |\sin{2|x|}|, \ x\in \left[-\frac{\pi}{4},\frac{\pi}{4} \right]"
I can't sketch these without a calculator which is a big problem. I can't seem to find a good source of modulus questions.

Thanks very much (hopefully someone else besides myself can find this practice useful).

Edit Yikes. Sorry for the latex not turning out right. I thought it'll work..
The thread I was referring to with the questions is this one: http://vcenotes.com/forum/index.php/topic,5600.0.html

[shinny]

Try differentiating modulus functions too - these really caught me off guard in a SAC =\ I know that the Essential textbook teaches how to do this, but I don't know which others do as well.

[/0]

Hmmm, yeah well I would concentrate firstly on any that has modulus signs around it. As long as every in the expression has modulus signs around it, you know the graph to the left of the y-axis is a reflection of the graph to the right of the y-axis. If the entire expression has modulus signs around it, then the expression can never be negative.

e.g.

First I would focus on the graph of (Which is the same as ). As the modulus sign is around the whole expression, you know the graph must never be negative, so every time you get a negative bit, reflect about the x-axis. Then, the minus sign in simply requires you to flip everything about the x-axis again.

In , both the and the expression have modulus signs around them, so just draw a normal , but make sure that the graph to the left of the y-axis is a reflection of the graph to the right of the y-axis and never negative.

[Mao]

Try differentiating modulus functions too - these really caught me off guard in a SAC =\ I know that the Essential textbook teaches how to do this, but I don't know which others do as well.

typically,

however, it is FAR easier to express and then differentiate the two pieces.

[shinny]

Yeh that's the way I learnt to do it. Another was to do composite functions but hybrid seems easier.

[dehaitest]

Thanks DivideBy0. If I come across anything else I'll post it here for anyone who's interested.

@Mao: What do you mean by "sign(x)"? Sorry I'm a bit slow; I'm a bit tired now (lol @ time).

[Mao]

the function sign(x) returns the sign of x. where x is negative, sign x returns -1, where x is positive, it returns 1. sign(x) is defined as 0 when x=0.
e.g.
sign(-4) = -1, sign(5) = 1, sign(0) = 0

algebraically,

hence, for non-zero values of x,

[dehaitest]

the function sign(x) returns the sign of x. where x is negative, sign x returns -1, where x is positive, it returns 1. sign(x) is not defined for x=0.
e.g.
sign(-4) = -1, sign(5) = 1, sign(0) = undefined

algebraically,

Ah right. Thanks very much for that explanation.

[humph]

the function sign(x) returns the sign of x. where x is negative, sign x returns -1, where x is positive, it returns 1. sign(x) is not defined for x=0.
e.g.
sign(-4) = -1, sign(5) = 1, sign(0) = undefined

algebraically,

Actually, .
Then we have that

See http://en.wikipedia.org/wiki/Sgn

[Mao]

my bad

[MikeOxlong]

wow... ive neva even seen any of that!! wat are the chances that will come up??

[Collin Li]

wow... ive neva even seen any of that!! wat are the chances that will come up??

I've never seen the sign function either, until this year, and I did Methods in 2006 and did quite well. Just be careful. If you're differentiating a function inside modulus signs, split up the modulus into a hybrid function first, then differentiate both parts. That's how I would have dealt with them.

[shinny]

I don't think you'll even be allowed to use the sign function. I'd say stick with hybrid functions in the extremely unlikely case this ever comes up...it's easier than playing around with another modulus in the derivative <_<