Flashcard 10 - Next Generation Advanced Algebra and Functions Flashcard Set for the ACCUPLACER Test

Vertical asymptotes result from division by 0.

Horizontal asymptotes arise in rational functions that have variables of the same degree in the numerator or denominator, or when the degree of the numerator is smaller than the degree of the denominator.

Other undefined portions arise from division by 0, which give points of discontinuity because the discontinuity can be factored out, or in radical functions, where negative values inside a radical cannot yield real values.

Identifying the points and lines of discontinuity simplify the graphing process, and give critical portions of a function that can help determine end behavior.