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Q. 114

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Precalculus Enhanced with Graphing Utilities

Found in: Page 197

Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

Can the graph of a polynomial function have no y-intercept? Can it have no x-intercepts? Explain.

When a polynomial does not have the constant term then the graph of the polynomial does not contain $y -$ intercept.

The graph of polynomial does not have $x -$ intercept if the roots of the polynomial function are imaginary.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Condition for having no y- intercept

When a polynomial does not have the constant term then the graph of the polynomial does not contain $y -$ intercept.

The graph of polynomial does not have $x -$ intercept if the roots of the polynomial function are imaginary.

Step 2. Condition for having no x- intercept

The graph of polynomial does not have $x -$ intercept if the roots of the polynomial function are imaginary.

For example The graph of $1 + x + x^{2}$ does not have $x -$ intercept.

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