The question asks "State whether the function is a polynomial, a rational function (but not a polynomial), or neither."

This is the function:

It looks rational, but apparently the answer is 'neither'. Why is this the case? Thanks.

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- July 12th 2010, 03:25 AMGlitchPolynomials and rational functions
The question asks "State whether the function is a polynomial, a rational function (but not a polynomial), or neither."

This is the function:

It looks rational, but apparently the answer is 'neither'. Why is this the case? Thanks. - July 12th 2010, 03:31 AMrunning-gag
Hi

This is due to the exponent 3/2

To get a rational function you must have only integer exponents - July 12th 2010, 03:32 AMGlitch
Ahh, thanks!

- July 12th 2010, 03:33 AMGlitch
Oh, also, does a polynomial have to have to have integer exponents?

- July 12th 2010, 03:37 AMrunning-gag
Yes

- July 12th 2010, 03:50 AMrunning-gag
Some examples

is NOT a polynomial

is a polynomial

is NOT a rational function

is a rational function

Now a more tricky example

is a rational function

But since is equal to 0 when x=1, you can factor out x-1

Therefore which is a polynomial

Actually and are not totally equal since the first one is defined for all real except 1 whereas the second one is defined for all real

The 2 functions are equal except on x=1