jinny1's Methods Questions Thread :D

[jinny1]

Hey guys just a quick question here

How would you split modulus functions into two equations to make it easier to draw absolute function graphs when the powers are greater than 1 (non-lineal)??

such as l(x-1)^2 -1l

or l(x-1)^3-1l

Thanks!!!!!

because if i do it the same way i spilt up linear functions, then i get a weird answer...

[pi]

I think its easiest to draw the original function and flip over the part below zero, rather than splitting (which will have the same result anyway, just in fancy writing).

[jbebbo]

Hey guys just a quick question here

How would you split modulus functions into two equations to make it easier to draw absolute function graphs when the powers are greater than 1 (non-lineal)??

such as l(x-1)^2 -1l

or l(x-1)^3-1l

pi's method for this is the best and easiest, but if you were interested, you would split |(x-1)^2-1| up like this:
(x-1)^2-1 for (x-1)^2-1>0, and
-((x-1)^2-1) for (x-1)^2-1<0
then you would solve the intersections:
(x-1)^2-1=0 => x=0 or x=2
then graph the function, and you find that y>0 for xE(-inf,0)U(2,inf) and that y<0 for xE(0,2)
therefore,
 l(x-1)^2 -1l= (x-1)^2-1 for xE(-inf,0]U[2,inf)
                    -(x-1)^2+1 for xE(0,2)

Moderator action: removed real name, sorry for the inconvenience

[jinny1]

Thanks guys. But in an exam how wud i do ur method because i wud end up drawing like 3 different graphs in the one plane and it will look confusing. Do u draw in pencil and rub the old one out or something?

[Greatness]

Draw in the function without the absolute values in a diff colour or dotted lline and indicate that it's not the modulus eqn. THen use another colour or a solid line and like what pi said, flip it into the postive side of the X axis. That should get you the marks, oh dont forget to add in intercepts and stuff.

Moderator action: removed real name, sorry for the inconvenience

[jbebbo]

If given working space, generally I just draw a tiny set of axis and draw the graph so I know where it is positive and negative, then i would draw the modulus graph on the axis provided. But whichever method is quickest for you is probably the best

[jinny1]

Thanks. The reason i used the spilt/hybrid method is because i have absolute no idea how to dilate a function when the dilation factor is placed outside the modulus. Something like 3l(x-1)^2-1l ....... I mean after u find all the key points to draw stuff inside the modulus, the dialtion factor would mean all these number wud be altered so u have to recalculate. Which i dont know if 3 is placed outside do u just time all the key x-points by 3??

[jbebbo]

When the 3 is outside the modulus, you would have to multiply all the y coordinates by 3 when drawing the graph

[jinny1]

i was just wondering, in the exam when you are writing the general solutions for a sin/cos/tan equations. Do you have to put the " 'n' is an element of 'Z' " Because i always forget. would you lose marks for that??

[jane1234]

i was just wondering, in the exam when you are writing the general solutions for a sin/cos/tan equations. Do you have to put the " 'n' is an element of 'Z' " Because i always forget. would you lose marks for that??

I think so, as it is part of the solution (and an essential one at that, n can't be something like 2.4356754). Do enough questions and you'll start remembering to put it in

[jinny1]

errrrr... it doesnt help that my maths teacher doesn't really care whether i put it in or not

[jane1234]

errrrr... it doesnt help that my maths teacher doesn't really care whether i put it in or not

But the unforgiving VCAA examiners will...

[RobM8]

always put the n E Z in, otherwise your answer is not a general solution.

[jinny1]

always put the n E Z in, otherwise your answer is not a general solution.

Can i just just put it in my final answer not during working out???

[pi]

always put the n E Z in, otherwise your answer is not a general solution.

Can i just just put it in my final answer not during working out???

Best to do this when you first introduce 'n'