Understanding Sine Function Transformations

This video tutorial explains how to graph a transformation of the sine function using the equation y = a * sin(bx + c) + d. It covers the significance of each parameter: amplitude, period, phase shift, and vertical shift. An example is provided to demonstrate the process of transforming the equation and graphing the function, including factoring and using the negative angle identity. The tutorial concludes with a step-by-step guide to sketching the graph, considering reflections and shifts.

What does the absolute value of 'a' represent in the sine function transformation?

• The vertical shift of the function

• The phase shift of the function

• The amplitude of the function

• The period of the function

If 'a' is negative, what happens to the graph of the sine function?

• It shifts horizontally

• It reflects across the midline

• It shifts vertically

• It remains unchanged

In the example function, what is the first step to handle a negative 'b' value?

• Add a constant to the function

• Factor out a negative from the equation

• Ignore the negative sign

• Multiply the function by a constant

What is the period of the function y = 2sin(-πx + 2π) + 0.5 after transformation?

• 2 units

• 1 unit

• 4 units

• π units

How is the phase shift determined in the transformed sine function?

• By the value of 'b' divided by 'c'

• By the value of 'd'

• By the value of 'a'

• By the value of 'c' divided by 'b'

What is the vertical shift in the function y = 2sin(πx - 2π) + 0.5?

• Down 1 unit

• Up 0.5 units

• Down 0.5 units

• Up 1 unit

Where does the midline of the graph lie after the vertical shift?

• y = 0

• y = 1

• y = 0.5

• y = -0.5

What is the maximum value of the function after considering the amplitude and vertical shift?

• 2.5

• 1.5

• 3.5

• 0.5

How many sub-intervals should the period be divided into for accurate graphing?

• Two

• Three

• Four

• Five

What pattern does the graph follow due to the reflection across the midline?

• Minimum, midline, maximum, midline

• Maximum, midline, minimum, midline

• Midline, minimum, midline, maximum

• Midline, maximum, midline, minimum