(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.
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Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
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