Understanding Polynomial Functions

The video tutorial covers the basics of polynomial functions, focusing on cubic functions. It explains the structure of polynomial functions, including exponents and coefficients, and provides examples of polynomial functions of various degrees. The tutorial demonstrates how to graph cubic functions using a T table and technology, highlighting the impact of additional terms on the graph's shape. An interactive exploration with sliders shows how changing coefficients affects the graph, providing a hands-on understanding of polynomial behavior.

What is the primary goal when graphing cubic functions as mentioned in the video?

• To graph them using only a ruler

• To graph them without any tools

• To graph them using technology

• To graph them by hand only

What are the exponents in a polynomial function?

• Any positive integer

• Any real number

• Any negative integer

• Any non-negative integer

Which of the following is a polynomial function of degree 1?

• F(x) = -4

• F(x) = 3x - 8

• F(x) = x^2 - x - 12

• F(x) = -x^3 + x^2 - 3x + 7

What is the degree of the function F(x) = -x^3 + x^2 - 3x + 7?

• Degree 2

• Degree 1

• Degree 0

• Degree 3

What is the first step in graphing a basic cubic function by hand?

• Use a calculator

• Make a T table

• Draw a straight line

• Estimate the curve

What is the result of cubing the number -2?

• 8

• 0

• -4

• -8

How does adding the term -4x to a cubic function affect its graph?

• It makes the graph linear

• It adds more curves

• It has no effect

• It makes the graph a straight line

What tool is suggested for accurately graphing complex cubic functions?

• A ruler

• Technology

• A protractor

• A compass

What does changing the value of 'A' in a cubic function affect?

• The graph's behavior

• The color of the graph

• The x-intercept

• The y-intercept

What is the effect of changing the value of 'D' in a cubic function?

• It alters the degree

• It changes the x-intercept

• It affects the y-intercept

• It changes the slope