How do you determine the phase shifts for sine and cosine graphs

The video tutorial covers transformations of functions, focusing on horizontal and vertical shifts, and phase shifts in trigonometric functions. It explains how to calculate these shifts using equations and highlights the importance of understanding the period of trigonometric functions. The tutorial provides examples and emphasizes the cyclical nature of sine and cosine graphs.

What happens to the graph of y = (x - 2)^2 compared to y = x^2?

• It shifts 2 units down.

• It shifts 2 units up.

• It shifts 2 units to the right.

• It shifts 2 units to the left.

In the equation y = a * sin(Bx - C) + D, what does a positive C indicate?

• The graph shifts to the right.

• The graph shifts to the left.

• The graph shifts upwards.

• The graph shifts downwards.

How is the period of a trigonometric function determined?

• By the value of D.

• By the value of A.

• By the value of B.

• By the value of C.

What is the period of the function y = cos(πx + π)?

• 2π

• π

• 2

• 1

How do you determine the phase shift of a function?

• By integrating the function.

• By calculating the derivative of the function.

• By finding the maximum value of the function.

• By setting the function's equation to zero.

What is the initial starting point of a sine or cosine graph?

• At π

• At 2π

• At -π

• At 0

If a graph starts at x = -1 instead of 0, what does this indicate?

• A phase shift of 1 to the right.

• A vertical shift of 1 unit down.

• A phase shift of 1 to the left.

• A vertical shift of 1 unit up.