Graphing Polynomial Functions: Key Concepts and Techniques

This video tutorial covers graphing polynomial functions, focusing on their characteristics, types, end behavior, and attributes. It explains the concepts of relative extrema, zeros, and intervals of increase and decrease. The tutorial also delves into the multiplicity of roots and how it affects graph behavior. Finally, it provides instructions on graphing polynomials using these concepts.

Which of the following is a characteristic of a polynomial function?

• It is continuous and smooth.

• It has cusps.

• It has sharp turns.

• It has gaps and breaks.

What is the degree of a linear function?

• 0

• 2

• 3

• 1

How do the ends of a quadratic function behave?

• They end in the same direction.

• They form a horizontal line.

• They end in opposite directions.

• One end goes up, the other goes down.

What happens to an even degree polynomial function as x approaches negative infinity?

• y oscillates.

• y remains constant.

• y approaches positive infinity.

• y approaches negative infinity.

What is a relative maximum in a polynomial function?

• A turning point where the function changes from increasing to decreasing.

• The highest point on the entire graph.

• A point where the function changes from decreasing to increasing.

• A point where the function crosses the x-axis.

What are the zeros of a polynomial function?

• Points where the function is undefined.

• Points where the function crosses the x-axis.

• Points where the function has a relative minimum.

• Points where the function has a relative maximum.

How does a polynomial function behave at a root with even multiplicity?

• It remains constant.

• It bends at the root.

• It bounces off the x-axis.

• It crosses the x-axis.

What is the degree of the function f(x) = (x - 4)^2 * (x + 1)?

• 3

• 2

• 4

• 5

How do you determine the end behavior of a polynomial function?

• By looking at the leading coefficient and the degree of the polynomial.

• By counting the number of roots.

• By finding the relative extrema.

• By checking the x-intercepts.

What is the maximum number of turning points a polynomial of degree n can have?

• n+1

• n-2

• n-1

• n