Exploring the Graphs of Polynomial Functions

What are the different terms used to refer to the zeros of a polynomial function?

• Zeros, factors, x-intercepts, solutions

• Zeros, roots, x-intercepts, solutions

• Zeros, roots, y-intercepts, solutions

• Zeros, roots, x-intercepts, factors

In the context of polynomial functions, what does it mean when the graph touches or crosses the x-axis?

• It indicates the zeros or roots of the function.

• It indicates the points where the function is undefined.

• It indicates the maximum or minimum points.

• It indicates the y-intercepts.

What is the first step in factoring the polynomial f(x) = x^3 + 3x^2 - x - 3?

• Multiply by a constant.

• Divide by x.

• Regroup the terms.

• Find the common factor.

What are the roots of the polynomial f(x) = x^3 + 3x^2 - x - 3 after factoring?

• 1, -3, 3

• -1, 1, -3

• 1, -1, 3

• -1, 1, 3

What is the special characteristic of the polynomial f(x) = -x^4 + 4x^3 - 4x^2 after factoring?

• It has squared factors.

• It has a leading coefficient of 1.

• It has a common factor of x.

• It has no real roots.

What does it mean when a graph 'bounces' at a zero?

• The zero is a rational number.

• The zero has an odd multiplicity.

• The zero has an even multiplicity.

• The zero is a complex number.

How does the graph behave at zeros with odd multiplicities?

• It forms a vertical asymptote.

• It touches and turns around.

• It crosses the x-axis.

• It remains constant.

What is the multiplicity of the zero at x = 3/2 in the given example?

• 3

• 4

• 2

• 1

What happens to the graph at x = -1 in the given example?

• It remains above the x-axis.

• It forms a cusp.

• It crosses the x-axis.

• It bounces off the x-axis.

What is the effect of higher multiplicities on the graph at a zero?

• The graph oscillates.

• The graph forms a vertical asymptote.

• The graph becomes more flattened out.

• The graph becomes steeper.