Maths Question (1 Viewer)

[professorayton8]

Hi :

 

[professorayton8]

Sorry... here's my question:im not really getting how to graph functions where you have to find the intercept, the asymptote, even/odd function etc.i get how to find those out, but im not sure how you are meant to graph it. I NEED HELP :Sthankyou

 

[professorayton8]

e.g- how would you graph y= 3 over x squared minus 4?

 

[Carrotsticks]

1. Draw the curve:



Which is a Hyperbola with the negative branch flipped upwards to become positive. Note that it has more 'extreme' values due to the fact that it's x squared not just x.

2. Shift it down by 4 units to acquire:

 

[Demento1]

1. Draw the curve:



Which is a Hyperbola with the negative branch flipped upwards to become positive. Note that it has more 'extreme' values due to the fact that it's x squared not just x.

2. Shift it down by 4 units to acquire:

Just wondering Carrotsticks, do you think the person could be referring to ?

 

[Carrotsticks]

Just wondering Carrotsticks, do you think the person could be referring to ?

Quite possibly.

If so, then I'm not going to bother re-doing the question. If OP can't be bothered typing the question properly, then I can't be bothered doing the question for them.

 

[professorayton8]

I'm sorry, I was meaning 3 over the whole thing (x squared minus 4)

 

[RealiseNothing]

I'm sorry, I was meaning 3 over the whole thing (x squared minus 4)

The x asymptotes are 2 and -2, the y asymptote is 0 (tell me if you don't know how I got this).

Find the y intercept by putting x=0:



Now the graph always tends towards the asymptotes. So it crosses the x axis at and go downwards on either side and approaches the lines x=-2 and x=2.

To the right and left of x=2 and x=-2 respectively, the graph becomes always positive, so it will always be above the x axis in these regions. Now just let them approach the two asymptotes.

 

[nightweaver066]

You could follow the exact same steps i posted here:

http://community.boredofstudies.org/showthread.php?t=282147&p=5842946#post5842946

 

[Timske]

http://www.wolframalpha.com/input/?i=y%3D3%2F%28x^2+-+4%29

lol

 

[professorayton8]

Thank you! I'm just wondering what 'symmetrical about the y axis and the origin' mean because it said in my textbook you have to find out if the fuction is odd/even/neither and if it's even then it's symmetrical about the y axis and if it's odd it's symmetrical about the origin. Thanks

 

[RealiseNothing]

Thank you! I'm just wondering what 'symmetrical about the y axis and the origin' mean because it said in my textbook you have to find out if the fuction is odd/even/neither and if it's even then it's symmetrical about the y axis and if it's odd it's symmetrical about the origin. Thanks

Symmetrical about the y axis means that the y axis cuts the function in half (well that's what it looks like).

Symmetrical about the origin is when the function is rotated 180 degrees around the origin.

 

[fishrushed]

Thank you! I'm just wondering what 'symmetrical about the y axis and the origin' mean because it said in my textbook you have to find out if the fuction is odd/even/neither and if it's even then it's symmetrical about the y axis and if it's odd it's symmetrical about the origin. Thanks

if you were asked to answer that question, a quicker way would be to let y= f(x), and then find f(-x). if f(-x)=f(x) then it is an even function. if f(-x)=-f(x) then it is an odd function. if f(-x) equals to anything other than f(x) itself or -f(x) , it is neither even or odd .
this is assuming that u have learnt function notation, which is taught along with even and odd functions, maybe before.