Drawing and interpreting curves

[sgx100]

How do u solve the following question

Draw f(x) = |x|^2 - |x| - 2
OR
Draw f(x) = |x^2 - x - 2|

Can anyone give out the basics of curves.....ie......lines,parabolas and drawing of curves out of functional equations like above

Please help...i went through all the threads....but cud not find anything on curves...driving me crazy...Quants guru plz help

[anurag01232006]

You have to first of all remove the mods.
Make two case as you make in normal mods questions.

CASE 1:when |x|<=0 & CASE 2:when |x|>=0.

You will get two different quadratic equations from the above two cases.Now you have to make the graphs.It will be a parabola of course but you have to consider the equations case wise..First of all take case one and get the abscissa and ordinate of that parabola by (-b/2a,-D/4a)..After that make the parabola in the coordinate plane but only in that x which is satisfied by the case i.e,if you have taken the case x>=0 then make the graph for positive side of x-axis only.Do this for the second part also..


By solving the above problem you will get a W-shape graph..try it and then tel me.Thanx.

[fultoo_bakar]

Originally Posted by sgx100

How do u solve the following question

Draw f(x) = |x|^2 - |x| - 2

Remove the mod from the square term becuase (-x)^2 and x^2 are same then the equation reduces to x^2+|x|-2=0
now solve x^2+x-2 for x>0
and x^2-x-2 for x<0

reduces to (x-2)(x+1) x<0
and (x+2)(x-1) x>0

Originally Posted by sgx100

OR
Draw f(x) = |x^2 - x - 2|

take reflection of x^2-x-2 = 0 where the curve is below the y axis.

Please do not open new threads for personalized queries. post your queries in quant specific threads...............

[rosh!]

Hi fultoo,

Thanks for your reply man....However, I think that this topic is one that has never been discussed in any thread and forms a basis for too many questions. Therefore, having a thread for this topic will help us focus on the topic and concentrate all the questions at one place.

I would request the mods to let this thread run and the junta to pour in their fundas about this.

Thanks!

[fultoo_bakar]

Originally Posted by rosh!

Hi fultoo,

Thanks for your reply man....However, I think that this topic is one that has never been discussed in any thread and forms a basis for too many questions. Therefore, having a thread for this topic will help us focus on the topic and concentrate all the questions at one place.

I would request the mods to let this thread run and the junta to pour in their fundas about this.

Thanks!

well if you want this thread ticking then here are some more
if y = f(x) is given then draw the following

1. y = f(|x|)
2. y = |f(x)|
3. |y| = f(x)
4. x = f(y)
5. y = f(x+a) where a is real and > 0
6. y = f(x) + a

if you somehow practice these you will be able to draw any curve(expect involving greatest interger).........................

the above 2 graphs are instances of 1 and 2.

[sgx100]

Originally Posted by rosh!

Hi fultoo,

Thanks for your reply man....However, I think that this topic is one that has never been discussed in any thread and forms a basis for too many questions. Therefore, having a thread for this topic will help us focus on the topic and concentrate all the questions at one place.

I would request the mods to let this thread run and the junta to pour in their fundas about this.

Thanks!

wrt to rosh n fultoo

well even i perceive that graphs for some reasons hv not found one dedicated thread or for that matter any decent consideration on any of the major quant threads. wud it be nice if this thread is left open for discussion on the same. fultoo has already posted some questions on it...maybe some more puys can drop in with their graphical blues...
i hv some questions with me...i can post those questions here....in case the mods decide to close down this thread....i wl post it on the Official Quant 2007 thread.

So what say puys....pull out some questions...and lets straighten out some lines

cheers
sgx100 ...soon going to be 200 ...he he LOL

[sgx100]

Fultoo, I cud draw all barring 3. and 4.
Can u help me with it.fultoo,anurag

Also some more questions on graphs

1. Draw f(x^2) = |x^2-2x|
2. Max (5+x,x^2-4,5-x)

Cheers
sgx

Originally Posted by fultoo_bakar

well if you want this thread ticking then here are some more
if y = f(x) is given then draw the following

1. y = f(|x|)
2. y = |f(x)|
3. |y| = f(x)
4. x = f(y)
5. y = f(x+a) where a is real and > 0
6. y = f(x) + a

if you somehow practice these you will be able to draw any curve(expect involving greatest interger).........................

the above 2 graphs are instances of 1 and 2.

[fultoo_bakar]

Originally Posted by sgx100

Fultoo, I cud draw all barring 3. and 4.
Can u help me with it.fultoo,anurag

Cheers
sgx

3. |y| = f(x)
suppose f(x) is 2 then y can take +2 and -2, moreover f(x) can never take negetive values. hence erase the f(x) below x axis and take mirror image about X axis of the part which is above x axis.
deepak.jpg
here the red line is for y = f(x)
and the black line is for |y| = f(x)

4. x=f(y).
x = f(y) is nothing but y = f inverse x
which can be obtained by taking mirror image about y = x.

[sdpkm.dee]

Can anyone help me with drawing of y=sin(x-y) ?