functions (2 Viewers)

[maths lover]

ok so this is the last question in my homework which i cant seem to sketch and hence cant find the domain and range. the curve is y=X^2(X^2-4) THANKS TO EVERYONE WHO HAS HELPED ME.

 

[davidbarnes]

Set up a table of values and do some test values (for X = -3 to 3 say).

 

[maths lover]

i was gunna do that but my teacher specifically said that we shouldn't use table of values

 

[SpiralFlex]

I will assume you don't know how to find stationary points and points of inflexion yet necessary to sketch the curve.

So I will give you a simple effective menu. First note,

If the function has a degree of 1, there will be a smooth line through the intercept.

If the function has an even degree, the curve will bounce off the intercept.

If the function has an odd degree (excluding 1), there will be a little hump on the intercept.

So, factorise first

So there are zeros (x intercepts) at 0, -2, 2

Now to sketch the curve, since the curve's highest degree is , and the coefficient of it is positive, you start at the top right corner. Place your pencil there. Otherise, if the coefficient of the highest degree is a negative place your pencil at the bottom.

Now, the first intercept, , there is a degree of 1, so draw a smooth line through it.

Now the second intercept , there is a degree of 2, the curve will bounce back.

Now the third intercept , there is a degree of 1, so draw a smooth line through it.

You will find the domain is all real x, and range is

EDIT: Sorry I made a mistake, let me redo question. I don't think it's possible without calculus.



For stationary points



Stationary points at <- Maximum turning point , <- Minimum turning point and <- Minimum turning point

 

[maths lover]

thanks spy yeah but we have done the way even and odd functions act when they meet intercepts i think

 

[maths lover]

just realised we have learnt the way they bounce and stuff at different degrees

 

[SpiralFlex]

just realised we have learnt the way they bounce and stuff at different degrees

Once you learn calculus, you will be able to sketch these types of graphs in much more detail, but for now all you really need to find the domain and range is the general shape of the graph and the intercepts.

thanks spy yeah but we have done the way even and odd functions act when they meet intercepts i think

I think you got confused with the terminology, finding even and odd functions is a completely different topic, these are to do with general sketching of polynomials with higher degrees.

 

[Deep Blue]

The domain is all real x, and range is y≥4.

 

[SpiralFlex]

The domain is all real x, and range is y≥4.

Are you sure it's not -4?

 

[SpiralFlex]

Mathslover, I might have made a mistake somewhere in my solution, please verify the answer with your teacher.

 

[Deep Blue]

Are you sure it's not -4?

Of course, that's what I meant.

 

[SpiralFlex]

Of course, that's what I meant.

For a minute there I thought I did something wrong.

 

[maths lover]

ok so that means i cant find the range without calculus

 

[SpiralFlex]

If you want, I can teach you the calculus method but that might be going too far.

 

[maths lover]

i dnt know is that the only way of finding the range

 

[SpiralFlex]

Yes, I think that's the only way to find it. I am not too sure though, probably ask a HSCer, they would probably know how to do it without calculus. Is this from the Fitzpatrick book by the way?

 

[maths lover]

ok then thanks anyways

 

[maths lover]

nah my teacher writes homework booklets for us so i dnt know what book it is from

 

[SpiralFlex]

ok then thanks anyways

No worries, if you need help just ask, I am sure that if I can't answer it, there will be HSCers who can.

"Asking is the fastest way of learning." SpiralFlex

 

[maths lover]

if anyone knows how to find the range without calculus please tell me