Understanding Polynomial Functions

The video tutorial explains how to complete a table of values for the function f(x) = x^3 - 4x and use these values to graph the function. It begins by substituting different x-values into the function to find corresponding y-values, which represent points on the graph. The tutorial then demonstrates how to plot these points and draw the graph, highlighting the function's behavior, including its turns. The video concludes with observations about the graph's characteristics, such as the number of turns, which relate to the function's degree.

What is the function given in the video?

• f(x) = x^3 + 4x

• f(x) = x^2 + 4x

• f(x) = x^3 - 4x

• f(x) = x^2 - 4x

What is the y-value when x = -2?

• -4

• 0

• 2

• 4

Which point is plotted for x = -1?

• (-1, -3)

• (-1, 1)

• (-1, 3)

• (-1, 0)

What is the y-value when x = 0?

• 0

• -1

• 4

• 1

Which point is plotted for x = 1?

• (1, 3)

• (1, 1)

• (1, 0)

• (1, -3)

What is the y-value when x = 2?

• 0

• 8

• 4

• -4

How many points are used to sketch the graph of the function?

• 3

• 4

• 5

• 6

What is the behavior of the graph as it passes through the x-axis?

• It starts high, turns, and ends high.

• It starts low, turns, and ends low.

• It starts low, turns, and ends high.

• It starts high, turns, and ends low.

What is a key feature of the graph of a degree 3 polynomial function?

• It has no turns.

• It has exactly one turn.

• It has at most two turns.

• It has at least three turns.

What is the maximum number of turns a polynomial function of degree n can have?

• n - 2

• n - 1

• n + 1

• n