Graph Transformations and Effects

This video tutorial covers transformations of cubic functions, starting with a review of the parent cubic function and its properties, such as the point of inflection, domain, and range. It then explains how transformations affect the graph of cubic functions, focusing on parameters D, C, and A. Parameter D causes vertical shifts, parameter C results in horizontal shifts, and parameter A affects vertical stretch, compression, and reflection. The video provides examples of these transformations and concludes with a recap of the key points.

What is the point of inflection for the parent cubic function?

• (1, 1)

• (-1, -1)

• (2, 2)

• (0, 0)

What happens to the graph of a cubic function when the parameter D is increased?

• It shifts left

• It shifts right

• It shifts up

• It shifts down

If the parameter C is negative, in which direction does the graph shift?

• Left

• Right

• Up

• Down

What effect does a negative value of parameter A have on the graph?

• Horizontal shift

• Vertical reflection

• Horizontal reflection

• No change

How does the graph change when the absolute value of A is a fraction between 0 and 1?

• Horizontal stretch

• Horizontal compression

• Vertical compression

• Vertical stretch

What is the result of a vertical stretch by a factor of 9?

• The graph shifts up

• The graph becomes narrower

• The graph becomes wider

• The graph shifts down

When X is subtracted by 2, in which direction does the graph move?

• Down

• Up

• Right

• Left

What happens to the inflection point when the graph is shifted to the right by 2 units?

• It moves to (-2, 0)

• It moves to (2, 0)

• It remains the same

• It moves to (0, 2)

If the parameter D is negative, what is the effect on the graph?

• It shifts left

• It shifts up

• It shifts down

• It shifts right

What is the new y-intercept when the graph is shifted left by 1 unit?

• It remains the same

• It moves to (1, 0)

• It moves to (0, 1)

• It moves to (-1, 0)