# Thread: Polynomial Functions

1. ## Polynomial Functions

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

2. Originally Posted by Cam5
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 ^^
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 ?

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.

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

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.

3. 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