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Q. 114

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Found in: Page 197

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# 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.

See the step by step solution

## 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.