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Rational functions domain ?

The domain of a rational function can’t be continuous right ?
Or is it ?

If it is, can someone please explain what a continuous domain is to me please

Reply 1

ghostwalker

Original post by JacobBob

The domain of a rational function can’t be continuous right ?
Or is it ?

If it is, can someone please explain what a continuous domain is to me please

A continuous domain is an interval, e.g.

-5 < x <\infty

. It may be finite, or infinite.

If you are considering the largest possible real domain for a rational function, then assuming the numerator and denominator are polynomials, the domain will be the entire real line, excluding the points where the denominator evaluates to zero.

e.g. f(x)=1/(x+4). Here the largest domain is the whole of the real line excluding x=-4. Not continuous.

If f(x)=1/(x^2-9), then it's the whole of the real line excluding x=3 and x=-3. Not continuous.

If f(x)=1/(x^2+9), then it's the whole of the real line and it is continuous - since the denominator is never zero.

Reply 2

Kallisto

Entertainment Forum Helper

Original post by JacobBob

The domain of a rational function can’t be continuous right ?
Or is it ?

If it is, can someone please explain what a continuous domain is to me please

As a rule, a rational function is restricted by the fraction in terms of the domain.

For example: f(x) = (x +1)/(x-3) is a rational function restricted by the number 3 for the domain, because 3 put in the denominator x - 3 leads to 0, what is undefined.

A continous domain exists, if the numbers of elements can take any value, but that isn't the case. It is discrete, so for putting values the funciton is defined.