Final answer:
To determine if a function is not rational, you need to look for characteristics inconsistent with rational functions, such as radicals, asymptotes, and exponents in the denominator.
Step-by-step explanation:
In mathematics, a function is considered rational if it can be expressed as a quotient of two polynomials, where the numerator and denominator polynomials have coefficients that are rational numbers.
To determine if a function is not rational, you need to look for any characteristics that are inconsistent with rational functions. These can include:
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For example, if a function has a square root or a cube root in it, it is not a rational function. Similarly, if there are vertical asymptotes or points where the function is undefined, it is not a rational function.
By examining the algebraic and graphical characteristics of a function, you can determine whether or not it is rational.