Understanding Cosine Function Transformations

The video tutorial explains how to find the equation of a function using sine or cosine. It begins by analyzing a graph to identify key features such as amplitude, period, and shifts. The tutorial focuses on determining the parameters a, c, and d by examining the graph's characteristics. It then calculates parameter b using the period of the function. Finally, the tutorial combines these parameters to write the complete equation of the function.

What is the role of the variable 'a' in the function equation?

• It determines the period of the function.

• It affects the vertical shift.

• It represents the amplitude.

• It affects the horizontal shift.

At x = 0, what is the maximum function value of the basic cosine function?

• Positive one

• Positive two

• Zero

• Negative two

What does the midline of the graph represent in this context?

• The maximum value of the function

• The y-axis

• The minimum value of the function

• The x-axis

If there is no vertical shift in the function, what is the value of 'c'?

• Positive one

• Negative one

• Positive two

• Zero

How is the period of the function determined from the graph?

• By counting the number of cycles in a given interval

• By measuring the horizontal distance of one complete cycle

• By finding the maximum value of the function

• By measuring the vertical distance between peaks

What is the period of the function if the horizontal distance from x = -6 to x = 0 is six units?

• Pi

• Six

• Twelve

• Three

What is the value of 'b' if the period is six?

• Pi over three

• Pi over six

• Two pi

• Three pi

What is the final equation of the function if a = 2, b = pi/3, c = 0, and d = 0?

• y = 2 * cos(x)

• y = cos(2 * pi/3 * x)

• y = 2 * cos(pi/3 * x)

• y = 2 * sin(pi/3 * x)

What does the variable 'd' affect in the function equation?

• The amplitude

• The period

• The vertical shift

• The horizontal shift

If there is no horizontal shift, what is the value of 'd'?

• Positive one

• Zero

• Negative one

• Positive two