Identify the transformations of sine

The video tutorial covers the identification and calculation of key transformations in mathematical equations, including amplitude, period, phase shift, vertical transformation, reflections, and domain and range. It explains how to calculate amplitude and period, understand reflections and phase shifts, explore vertical translations and domain, and graph transformations to determine the range. The tutorial emphasizes understanding the effects of these transformations on the graph.

What is the amplitude of a graph if the coefficient 'a' is 1/4?

• 1/4

• 2

• 4

• 1

How do you calculate the period of a graph with a coefficient B of 2?

• π/2

• π

• 2π

• 4π

What condition indicates a reflection about the X-axis?

• D is negative

• A is negative

• C is negative

• B is negative

How is the phase shift determined in a transformation equation?

• By identifying the vertical shift

• By calculating 2π/B

• By finding the absolute value of A

• By solving BX - C = 0

What does a vertical translation of -2 indicate about the graph?

• The graph shifts left by 2

• The graph shifts right by 2

• The graph shifts down by 2

• The graph shifts up by 2

What is the domain of a sine graph with transformations?

• -1 to 1

• All real numbers

• 0 to 2π

• π to 2π

If the original range of a sine graph is -1 to 1, what is the new range after a vertical compression by 1/4 and a downward shift by 2?

• -7/4 to -9/4

• -3/4 to 3/4

• -2 to 2

• -1/4 to 1/4