# Thread: Domain of Rational Functions

1. ## Domain of Rational Functions

Find the domain of f(x) = (2x)/(x - 2).

How is this done algebraically?

2. ## Re: Domain of Rational Functions

We see the only restriction that applies in this case is division by zero, so we exclude any values of $\displaystyle x$ which causes the denominator to be zero.

3. ## Re: Domain of Rational Functions

Originally Posted by MarkFL
We see the only restriction that applies in this case is division by zero, so we exclude any values of $\displaystyle x$ which causes the denominator to be zero.
So, the domain is ALL REAL NUMBERS except that x cannot be 2.

4. ## Re: Domain of Rational Functions

Originally Posted by harpazo
So, the domain is ALL REAL NUMBERS except that x cannot be 2.
Right. Generally: ........except all cases that create a denominator = 0
Take a / (b - c): except cases where b - c = 0 or except cases where b = c

5. ## Re: Domain of Rational Functions

I find the "division by zero" rule strange: why "not allowed"?

1 / (2 - 2) = no solution...division by zero...

1 * (2 - 2)^(-1) = 0

Get my drift?
Deb? Mark?

6. ## Re: Domain of Rational Functions

Your second equation still implies division by zero.

7. ## Re: Domain of Rational Functions

Agree...my point is 0 is given as answer by "all or some?" calculators.
UBasic language does anyhoo...

8. ## Re: Domain of Rational Functions

Originally Posted by DenisB
Agree...my point is 0 is given as answer by "all or some?" calculators.
UBasic language does anyhoo...
W|A returns what they call "complex infinity" for that expression.

9. ## Re: Domain of Rational Functions

Sweet...the old double post. I don't know what happened, I was flitting from tab to tab.

10. ## Re: Domain of Rational Functions

Well, was kinda kidding...if I want 0 returned from a division by 0,
all I need, easy to program...

11. ## Re: Domain of Rational Functions

Originally Posted by DenisB
Well, was kinda kidding...if I want 0 returned from a division by 0,
all I need, easy to program...
I would likely do something like:

if (c == 0)
{
a = 0;
}
else
{
a = b/c;
}

12. ## Re: Domain of Rational Functions

n = numerator, d = denominator, r = result

if d=0 then r=0 else r=n/d

That's UBasic; whatever yer usin' is too complicated for me

13. ## Re: Domain of Rational Functions

Interesting notes.