Graph Transformations and Effects

The video tutorial explains how to graph the function y = x^3 and apply transformations to it. It covers vertical stretching, horizontal and vertical shifts, and flipping the graph. The instructor demonstrates how to sketch the transformed graph and discusses the effects of different values on the graph's appearance. Key concepts include understanding the roles of a, H, and K in graph transformations.

What is the base function discussed in the video?

• y = x^3

• y = x^2

• y = x^4

• y = x

What does the 'a' value represent in graph transformations?

• Horizontal stretch

• Vertical shift

• Vertical stretch

• Horizontal shift

If 'a' is 3, what happens to the graph?

• It shifts up 3 units

• It stretches vertically by a factor of 3

• It shifts left 3 units

• It flips horizontally

What is the effect of a positive 'H' value on the graph?

• Shifts right

• Shifts left

• Stretches horizontally

• Stretches vertically

If 'H' is -4, in which direction does the graph move?

• Right 4 units

• Left 4 units

• Up 4 units

• Down 4 units

What does the 'K' value affect in the graph?

• Vertical shift

• Horizontal shift

• Vertical stretch

• Horizontal stretch

If 'K' is -1, what happens to the graph?

• It shifts down 1 unit

• It shifts up 1 unit

• It stretches vertically by a factor of 1

• It flips horizontally

How do you combine the effects of 'H' and 'K' on the graph?

• Shift right and up

• Shift left and down

• Shift right and stretch

• Shift left and stretch

What happens to the graph when 'a' is negative?

• It shifts left

• It flips vertically

• It stretches horizontally

• It shifts up

If 'a' is -1, what is the effect on the graph?

• Shifts right

• Flips vertically

• No change

• Stretches vertically