Transformations and Characteristics of Cubic Functions

The video tutorial covers the attributes and transformations of cubic functions, starting with the basic cubic function f(x) = x^3. It explains how to graph this function using a t-table and discusses its domain, range, and intercepts. The tutorial then explores various transformations, including vertical stretches, compressions, and reflections, as well as translations in different directions. It concludes by highlighting the common attributes of transformed cubic functions, such as their domain, range, and symmetry.

What is the parent function of a cubic function?

• f(x) = x^3

• f(x) = x

• f(x) = x^4

• f(x) = x^2

Which of the following is a characteristic of the parent cubic function?

• It has a maximum point.

• It is a linear function.

• It is symmetric about the origin.

• It has a minimum point.

How do you determine the y-values when graphing a cubic function?

• By adding 2 to each x-value.

• By subtracting 1 from each x-value.

• By squaring each x-value.

• By cubing each x-value.

What is the domain of the parent cubic function?

• All real numbers

• Only integers

• All negative numbers

• All positive numbers

What is the range of the parent cubic function?

• Only integers

• All real numbers

• All negative numbers

• All positive numbers

What is the x-intercept of the parent cubic function?

• (0, 0)

• (2, 8)

• (1, 1)

• (-1, -1)

What is the y-intercept of the parent cubic function?

• (2, 8)

• (0, 0)

• (1, 1)

• (-1, -1)

What transformation occurs when f(x) = 2x^3?

• Horizontal shift

• Vertical stretch

• Vertical compression

• Reflection over x-axis

What transformation occurs when f(x) = 0.25x^3?

• Horizontal shift

• Vertical stretch

• Vertical compression

• Reflection over x-axis

What happens when a cubic function is reflected over the x-axis?

• The graph is shifted up.

• The graph is flipped upside down.

• The graph is stretched.

• The graph is compressed.