What is this rational function?

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  f(x) = (x^2+2)/(x-1)

Step-by-step 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.

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step-by-step explanation: