Graph Transformations and Parameters

The video tutorial explains how to graph the function y = x^3 and apply transformations to it. It covers the effects of vertical stretching, horizontal and vertical shifts, and flipping the graph. The tutorial provides step-by-step instructions on how to sketch the transformed graph, emphasizing the roles of the parameters a, H, and K in these transformations. The video also includes examples to illustrate these concepts, helping viewers understand how each transformation affects the graph's appearance.

What is the base function being graphed in the video?

• y = x^2

• y = x^3

• y = x^4

• y = x^5

How does the parameter A affect the graph of y = x^3?

• It stretches or compresses the graph vertically.

• It rotates the graph.

• It shifts the graph vertically.

• It shifts the graph horizontally.

If A is greater than 1, what happens to the graph?

• It shrinks vertically.

• It stretches vertically.

• It shifts left.

• It shifts right.

What is the effect of the parameter H on the graph?

• It shifts the graph up.

• It shifts the graph down.

• It shifts the graph left or right in the opposite direction.

• It stretches the graph.

If H is -3, in which direction does the graph shift?

• Left 3 units

• Right 3 units

• Up 3 units

• Down 3 units

How does the parameter K affect the graph?

• It shifts the graph vertically.

• It shifts the graph horizontally.

• It stretches the graph.

• It flips the graph.

If K is positive, in which direction does the graph move?

• Up

• Down

• Left

• Right

What happens to the graph when A is negative?

• It flips horizontally.

• It flips vertically.

• It shifts down.

• It shifts up.

Which parameter is responsible for flipping the graph?

• H

• None

• K

• A

What is the overall effect of combining H, K, and A on the graph?

• Only shifts the graph.

• Only stretches the graph.

• Shifts, stretches, and possibly flips the graph.

• No effect.