Polynomial Functions

Cam5 · #1 $Old$ September 27th, 2008, 10:02 AM

Hey all,

I just had few questions that couldn't wait until I see my teacher to clear up. Hopefully someone won't mind explaining...

1. I've never encountered the symbol "|", as in (x | 2) . What does it mean, and how would I go about deciding it's use?

2. What role does 'K' play in the equation f(x) = k(x - s)(x - t)(x - u)etc.?
I know that if k is negative, we reflect the graph in the x-axis, but is it also (as I remember it) the term that will stretch the graph vertically?

3. An application question gives me a function $y = 26.55x^3 - 170.56x^2 + 249.62x + 1257.80$ , 0 < x < 4 and asks me to state the restricted domain... I'm not sure if it *is* 0 < x < 4, or what. It's just a guess, and I need an explanation really.

Thanks to anyone who takes the time to give me hand yet again!

- Cam

Moo · #2 $Old$ September 27th, 2008, 10:30 AM

Quote:

Originally Posted by Cam5 $View Post$

Hey all,

I just had few questions that couldn't wait until I see my teacher to clear up. Hopefully someone won't mind explaining...

Of course ^^

Quote:

1. I've never encountered the symbol "|", as in (x | 2) . What does it mean, and how would I go about deciding it's use?

It depends... Is "x divides 2" appropriate for you ?

Quote:

2. What role does 'K' play in the equation f(x) = k(x - s)(x - t)(x - u)etc.?
I know that if k is negative, we reflect the graph in the x-axis, but is it also (as I remember it) the term that will stretch the graph vertically?

Yes, sort of. Imagine f(x) represents the y-ordinate of any point. If you increase k, it means you increase f(x), that is to say for each point, you increase the y-ordinate. So it looks like you're stretching (or narrowing if you make k decrease) the curve.

Quote:

3. An application question gives me a function $y = 26.55x^3 - 170.56x^2 + 249.62x + 1257.80$ , 0 < x < 4 and asks me to state the restricted domain... I'm not sure if it *is* 0 < x < 4, or what. It's just a guess, and I need an explanation really.

Yes it is. You're told that this equation holds for 0<x<4. Thus it can be considered as the domain.
If you want an example of an application... hmmm let's see.

You can define a function as being :
$f(x)=\left\{\begin{array}{lll} 1257.8 \quad \text{ if $x \leq 0$} \\ -170.56x^2 + 249.62x + 1257.80 \quad \text{ if $0<x<4$}\\ 1336.86 \quad \text{ if $x \geq 4$} \end{array}\right.$

It means it takes these values if x is in the given domains.
In that case, the restricted domain of -170.56x^2 + 249.62x + 1257.80 is (0;4)

I hope it looks clear... If not, just ask.

Cam5 · #3 $Old$ October 3rd, 2008, 02:07 PM

Moo, you're always very helpful and prompt! Sorry for the delay in reply.
Thanks for taking the time once again to teach me something.

As is your style - I got more info than I bargained for - my questions were clarified, and I did end up solving my problems with a little more confidence and background info.

Cheers,

- Cam