Sine Function Transformations and Properties

The video tutorial explains how to transform and graph a sine function by identifying key values (C, A, B, D) and applying vertical and horizontal shifts. It covers calculating amplitude and period, graphing one period of the sine function, and analyzing phase shifts. The tutorial provides a step-by-step guide to understanding the transformation and graphing process, ensuring learners can accurately plot the sine function on a graph.

What is the value of C in the given sine function?

• -1

• 2

• 1

• 0

How does a positive value of C affect the sine function?

• Changes its period

• Shifts it down

• Shifts it up

• Reflects it

What is the amplitude of the sine function if A is -3?

• 3

• 0

• -3

• 6

How does a negative A value affect the graph of the sine function?

• Shifts it up

• Changes its period

• Shifts it down

• Reflects it across the midline

What is the period of the sine function if B is π/3?

• 6

• 3

• 2π

• π

How does a negative D value affect the graph of the sine function?

• Shifts it left

• Changes its amplitude

• Shifts it right

• Reflects it

What is the first step in graphing the sine function over one period?

• Divide the interval

• Determine the phase shift

• Identify the midline

• Calculate the amplitude

What is the pattern of the sine function when A is negative?

• Midline, maximum, midline, minimum

• Midline, minimum, midline, maximum

• Maximum, midline, minimum, midline

• Minimum, midline, maximum, midline

What is the translation of the point (0, 0) in the transformed sine function?

• (-1, 4)

• (0, 1)

• (4, -1)

• (-4, 1)

What is the minimum point a quarter of the period to the right of the phase shift?

• (1.5, 1)

• (2.5, 2)

• (-1.5, -1)

• (-2.5, -2)