Question

What is this rational function?

Answer 1

A rational function is any function which can be written as the ratio of two polynomial functions, where the polynomial in the denominator is not equal to zero. The domain of f(x)=P(x)Q(x) f ( x ) = P ( x ) Q ( x ) is the set of all points x for which the denominator Q(x) is not zero.

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Answer 2

9514 1404 393

Answer:

f(x) = (x^2+2)/(x-1)

Explanation:

In simplest form, it will be a quadratic divided by (x-1). The quadratic must have no zeros, and a y-intercept of 2.

One such could be ...

f(x) = (x^2 +2)/(x -1)

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The numerator polynomial must have no zeros in order to prevent the rational function from having zeros. It must be a function that has a degree an odd number greater than the denominator function. The denominator function can have only one zero, at x=1. The ratio of the functions must have a net odd degree and the overall leading coefficient must be positive in order to make the end behavior match the requirement.