Understanding the Cosine Function

The video tutorial explains how to analyze a cosine function by determining its vertical shift, midline, amplitude, period, and phase shift. It begins by rewriting the function in a standard form, factoring necessary components, and identifying key characteristics. The tutorial then calculates the period and phase shift, followed by graphing the function to verify the results. The process includes factoring expressions, understanding transformations, and using graphs to confirm the mathematical analysis.

What is the initial problem with the given cosine function?

• It is not in the form of a sine function.

• It has an incorrect period.

• It is not in the form of b times the quantity x minus d.

• It has an incorrect amplitude.

What is the purpose of factoring two from the expression?

• To adjust the vertical shift.

• To simplify the expression.

• To change the amplitude.

• To fit the expression into the desired form.

What is the value of 'a' in the rewritten cosine function?

• 10

• -2

• 2

• -10

How is the vertical shift determined in the cosine function?

• By the value of 'c'.

• By the value of 'b'.

• By the value of 'a'.

• By the value of 'd'.

What is the midline of the cosine function after the vertical shift?

• y = 0

• y = 3

• y = -3

• y = 10

What is the amplitude of the cosine function?

• 10

• 5

• 20

• 15

What is the period of the cosine function?

• π

• π/4

• 2π

• π/2

What is the phase shift of the cosine function?

• Right π/16 units

• Left π/16 units

• Left π/8 units

• Right π/8 units

What is the maximum value of the cosine function?

• 10

• 7

• 17

• 13

What is the pattern of the cosine function over one period after reflection?

• Minimum, midline, maximum, midline, minimum

• Midline, maximum, midline, minimum, midline

• Maximum, minimum, midline, maximum, minimum

• Maximum, midline, minimum, midline, maximum