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In my book we had 3 problems that we had to do for homework and none of my classmates could understand why the book answered them a certain way.

Question:

State whether the functions below are Rational, Polynomial, Neither, or Both.

1. f(x)=3x

^{2}+2x+1

2. f(x)=(2x

^{2}+4x)/(x-1)

3. f(x)=(x-1)

^{1/2}

From what I understand a rational function needs to have a fraction bar in it, so number two is rational. Number 3 is raised to the 1/2 power so it is neither. Not rational nor a polynomial. I thought that number one would just be a polynomial, but my teacher's book says it is both. We discussed it in class and couldn't make sense of it.

If someone could explain to me what the functions above are that would be very helpful.

Thanks!