a) Use the Intermediate Value Theorem to showW that if part of the graph of a polynomial function y = p(x) is located below the X-axis and above he X-axis, then it must intersect the X-axis at some number x = c. (This %3D umber c such that f(c) = 0 is called a zero of f(x)). In algebraic terms: it %3D or some numbers a, b, a < b, p(a) < 0 but p(b) > 0, then for some x in the nterval (a, b), p(x) = 0. (b) Then give an example of a polynomial p(x) vithout a zero (a zero is a number c such that p(c) = 0 ). c) Give an example of a function h(x) whose graph is above the X-axis nd below the X-axis, yet h(x) does not intersect the X-axis.

a) Use the Intermediate Value Theorem to showW that if part of the graph of a polynomial function y = p(x) is located below the X-axis and above he X-axis, then it must intersect the X-axis at some number x = c. (This %3D umber c such that f(c) = 0 is called a zero of f(x)). In algebraic terms: it %3D or some numbers a, b, a < b, p(a) < 0 but p(b) > 0, then for some x in the nterval (a, b), p(x) = 0. (b) Then give an example of a polynomial p(x) vithout a zero (a zero is a number c such that p(c) = 0 ). c) Give an example of a function h(x) whose graph is above the X-axis nd below the X-axis, yet h(x) does not intersect the X-axis.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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