(A) Let p(x) be a polynomial of degree n ≥ 1. Explain why each of the following is true:
(1) The graph of p(x) intersects any vertical line in exactly one point.
(2) The graph of p(x) intersects any horizontal line in at most n points.
(3) The graph of p(x) has neither horizontal nor vertical asymptotes.
(B) Discuss the graphs of
Use part (A) to explain why none of the graphs of f, g, h, or k is the graph of a polynomial function.
Want to see the full answer?
Check out a sample textbook solutionChapter 10 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
- Algebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning