Question

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

Short answer

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-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.