Graph Transformations and Shifts

The video tutorial explains how to graph functions using C and D transformations, focusing on phase and vertical shifts. It demonstrates graphing sine and cosine functions with specific transformations, using both visual and tabular methods to apply shifts. The tutorial covers the process of adjusting x and y values to reflect these transformations, providing a clear understanding of how to manipulate graphs.

What does the 'C' in the equation represent in graph transformations?

• Vertical shift

• Phase shift

• Amplitude change

• Frequency change

In the equation y = sin(x - 30°) + 3, what does the '+3' indicate?

• A shift to the left

• A vertical shift downwards

• A vertical shift upwards

• A shift to the right

How do you adjust the x-values when applying a phase shift of 30 degrees to the right?

• Add 30 to each x-value

• Subtract 30 from each x-value

• Multiply each x-value by 30

• Divide each x-value by 30

What is the new y-value if the original y-value is -1 and the graph is shifted up by 3?

• 1

• 2

• 0

• 3

Which of the following is a correct transformation for y = sin(x - 30°) + 3?

• Shift right 30°, down 3

• Shift right 30°, up 3

• Shift left 30°, up 3

• Shift left 30°, down 3

What is the starting point of the cosine graph after a left shift of π?

• 2π

• -π

• π

• 0

In the transformation y = cos(x + π) - 3, what does the '-3' signify?

• A vertical shift downwards

• A vertical shift upwards

• A shift to the right

• A shift to the left

How do you adjust the y-values when applying a vertical shift of -3?

• Multiply each y-value by 3

• Subtract 3 from each y-value

• Add 3 to each y-value

• Divide each y-value by 3

What is the effect of a phase shift to the left on the x-values?

• Subtract from each x-value

• Divide each x-value

• Multiply each x-value

• Add to each x-value

What is the final y-value if the original y-value is 0 and the graph is shifted down by 3?

• 0

• -3

• -1

• 3