This is a polynomial. Since *f*(*x*) is defined for every value of *x*, and there are no finite values of *a* (that is, actual numbers *a*) near which
*f*(*x*) keeps getting bigger and bigger and bigger, this function has no vertical asymptotes. If a rational function doesn't have a constant in the numerator, we do the same stuff as before: factor the numerator and denominator, simplify if possible, and find the roots of the denominator. The roots of the **simplified denominator** are the vertical asymptotes. If the value *x* = *a* only makes the denominator zero, the numerator acts like a finite number as *x* approaches *a*. Meanwhile the denominator gets crazy small, making the value of the function get crazy big. |