Mathematics

A proper rational function is one where the degree of the numerator is strictly less than the degree of the denominator—think of it as the "bottom growing faster than the top." This matters because proper rationals have nicer behavior: they approach zero as $x \to \infty$ and avoid certain complications in calculus and partial fractions. Check each option by counting the highest power in the numerator versus the denominator.

A proper rational function is one where the degree of the numerator is strictly less than the degree of the denominator—think of it as the "bottom growing faster than the top." This matters because proper rationals have nicer behavior: they approach zero as $x \to \infty$ and avoid certain complications in calculus and partial fractions. Check each option by counting the highest power in the numerator versus the denominator.