# Domain +Graphing

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• Jul 27th 2006, 11:49 PM
askmemath
Domain +Graphing
Quote:

I need to determine the domain, sketch the graph of each function and show/explain the connection between the graph and the domain:

g (x) = x^2
______________

x^2 + 2x - 3
x^2 + 2x-3 should be greater than 0 since (Any number)/0 is NOt Defined

(X+3)(X-1)>0
So either
X> -3 OR X>1

Thus domain becomes
(-3,1)u(1,Infinity)

Right?

Now how wld I graph and explain the connection??
• Jul 28th 2006, 04:17 AM
topsquark
Quote:

Originally Posted by askmemath
x^2 + 2x-3 should be greater than 0 since (Any number)/0 is NOt Defined

(X+3)(X-1)>0
So either
X> -3 OR X>1

Thus domain becomes
(-3,1)u(1,Infinity)

Right?

Now how wld I graph and explain the connection??

The values of x such that $\displaystyle x^2+2x-3=0$ are forbidden. NOT where $\displaystyle x^2+2x-3$ is negative. There are three parts to the domain.

Wherever the denominator goes to zero will be a vertical asymptote (unless the numerator also goes to zero at this value of x, which does not happen here).

-Dan
• Jul 28th 2006, 09:36 AM
askmemath
Quote:

Originally Posted by topsquark
The values of x such that $\displaystyle x^2+2x-3=0$ are forbidden. NOT where $\displaystyle x^2+2x-3$ is negative. There are three parts to the domain.

Wherever the denominator goes to zero will be a vertical asymptote (unless the numerator also goes to zero at this value of x, which does not happen here).

-Dan

Umm, So the domain becomes....??

And how would I be graphing this?
• Jul 28th 2006, 09:44 AM
ThePerfectHacker
Quote:

Originally Posted by askmemath
Umm, So the domain becomes....??

The domain is that "x" can be any number EXCEPT $\displaystyle -3,1$.

You can write it in three ways,
$\displaystyle x\in \mathbb{R}, x\not = -3,1$
Or,
$\displaystyle \left\{ \begin{array}{c}x<-3\\ -3<x<1\\ 1<x$
Or,
$\displaystyle x\in (-\infty,-3)\cup (-3,1) \cup (1,+\infty)$
• Jul 28th 2006, 09:52 AM
ThePerfectHacker
Quote:

Originally Posted by askmemath
And how would I be graphing this?

Step 1 draw vertical line which are asymptotes for the undefinied values. That means draw $\displaystyle x=-3,x=1$

Step 2 find how f(x) behaves as you approach one of these values from the left and right. Meaning, begin with the vertical asymptotes x=-3 first. As you approach the number -3 from the left what happens to f(x)? It gets bigger and bigger. That means it is approaching +infinity so you approach the asymptote line but you never pass it. Next what happens when you approach x=-3 from the left? It gets smaller and smaller. That means it is approaching -infinity so you approach the asymptote line but you never pass it and go down. The same approach use for x=1.