Understanding Polynomial Functions

What is the effect of a double root on the graph of a polynomial?

• The graph remains constant.

• The graph bounces off the x-axis.

• The graph has no x-intercept.

• The graph crosses the x-axis.

How does an odd multiplicity affect the graph of a polynomial at its root?

• The graph has no effect.

• The graph forms a loop.

• The graph crosses the x-axis.

• The graph bounces off the x-axis.

If a polynomial has a root at x = -3 with a multiplicity of 2, what happens at this point?

• The graph has no x-intercept.

• The graph forms a peak.

• The graph bounces off the x-axis.

• The graph crosses the x-axis.

What is the multiplicity of a root if the graph crosses the x-axis at that point?

• Zero

• Undefined

• Even

• Odd

Which of the following describes the end behavior of a polynomial with an even degree and a positive leading coefficient?

• The graph starts and ends in opposite directions.

• The graph starts and ends in the same direction.

• The graph has no end behavior.

• The graph forms a loop.

How does a negative leading coefficient affect the end behavior of a polynomial with an odd degree?

• The graph starts positive and ends negative.

• The graph starts and ends in the same direction.

• The graph has no end behavior.

• The graph starts negative and ends positive.

What is the degree of a polynomial if its highest power of x is x^4?

• 2

• 3

• 4

• 5

When graphing a polynomial, what is the significance of the y-intercept?

• It shows the multiplicity of the roots.

• It indicates the number of roots.

• It is the point where the graph crosses the y-axis.

• It determines the end behavior.

If a polynomial has zeros at x = 1 and x = -4, what are these points called?

• Peaks

• Vertices

• Intercepts

• Roots

What is the first step in graphing a polynomial in factored form?

• Plot the zeros.

• Identify the leading coefficient.

• Determine the y-intercept.

• Find the degree of the polynomial.