Math Question ! (1 Viewer)

[SGSII]

Hey Guys
can you help graph this:

1 / x^2 + 1

can you show step by step solution ?

Thanks !

 

[Carrotsticks]

Did you mean:



or

 

[SGSII]

^
The first option

 

[nightweaver066]

1. Make sure numerator is of lower degree than denominator
2. Odd/Even/Neither?
3. x & y intercepts
4. Vertical asymptotes
a) Test behaviour at vertical asymptotes
5. Behaviour as x -> + or - infinity

Using these steps, 1. is fulfilled.
2. f(-x) = f(x) so it is even (symmetrical about y-axis)
3. When x = 0, y = 1 so y intercept is (0, 1). When y = 0, 0 = 1 which cannot be possible so there is no y intercept and there is a horizontal asymptote at y = 0
4. Denominator cannot equal to zero as you cannot solve x^2 + 1 = 0
5. As x -> infinity, 1 / (x^2 + 1) -> 0+ (the plus meaning it is slightly above 0)
As x -> -infinity, 1 / (x^2 + 1) -> 0+

So now you're left with this,

From this, we can "join the dots" smoothly in to a nice curve.

 

[SGSII]

Ohh i see
Thaanks !

 

[Timske]

Bell curve straight away

 

[RivalryofTroll]

There's two methods available for use:
- As nightweaver said
OR
- The reciprocal method



Someone else can explain the reciprocal method.

 

[RealiseNothing]

A really weird way that you might be able to use (although probably much harder), is to graph , and then differentiate the graph since:





Use the graphing a derivative method or whatever it's called.

 

[professorayton8]

Hi! i have a similar question to the question asked in this thread.how do you know what the graph looks like when you find out all the asymptotes, intercepts etc.?and what does 'symmetrical about the y and origin' mean?- how does it affect the graph?thanks

 

[RealiseNothing]

Hi! i have a similar question to the question asked in this thread.how do you know what the graph looks like when you find out all the asymptotes, intercepts etc.?and what does 'symmetrical about the y and origin' mean?- how does it affect the graph?thanks

Well for asymptotes, the graph will always tend towards it.

 

[professorayton8]

so how would you graph y= 3x over x squared minus 4 ?

 

[Carrotsticks]

so how would you graph y= 3x over x squared minus 4 ?

If you have questions, make your own thread.

Best not to hijack somebody else's. The social equivalent would be you asking the teacher a question, then me suddenly butting in and asking my own one.

 

[professorayton8]

problem is... nobody is replying

 

[Carrotsticks]

problem is... nobody is replying

Be patient, you will get an answer.

 

[fishrushed]

so how would you graph y= 3x over x squared minus 4 ?

i take it that u haven't learnt differentiation?