Cubic Function Transformations Explained

The video tutorial covers cubic functions, focusing on transformations such as translations, vertical and horizontal stretches, and compressions. It explains how changes in parameters H, K, A, and B affect the graph of a cubic function. The tutorial includes examples to illustrate how to graph cubic functions with these transformations, emphasizing the importance of the anchor point and how to determine it.

What does the H value in a cubic function transformation represent?

• Horizontal stretch

• Vertical shift

• Horizontal shift

• Vertical stretch

If the transformation function is f(x) = (x - 3)^3, where is the anchor point on the x-axis?

• x = 1

• x = 0

• x = -3

• x = 3

What effect does a positive K value have on the graph of a cubic function?

• Moves the graph left

• Moves the graph right

• Moves the graph up

• Moves the graph down

What does the A value in a cubic function transformation indicate?

• Horizontal stretch

• Vertical shift

• Vertical stretch

• Horizontal shift

If A is negative in a cubic function, what happens to the graph?

• It shifts left

• It shifts right

• It inverts vertically

• It inverts horizontally

What happens to the graph of a cubic function when B is greater than 1?

• It stretches vertically

• It compresses vertically

• It stretches horizontally

• It compresses horizontally

In the function f(x) = (1/2x)^3, how many units does it take to go up one unit on the y-axis?

• 3 units

• 2 units

• 1 unit

• 4 units

For the function f(x) = 3(x + 1)^3 - 5, where is the anchor point?

• (1, 5)

• (-1, -5)

• (-1, 5)

• (1, -5)

In the function f(x) = -2(x - 4)^3 + 1, what is the vertical transformation?

• Stretch by 2

• Compression by 2

• Stretch by -2

• Compression by -2

For the function f(x) = (1/3x)^3 - 2, what is the horizontal transformation?

• Stretch by 1/3

• Stretch by 3

• Compression by 1/3

• Compression by 3