Understanding Cosine Functions and Their Properties

The video tutorial explains how to sketch the graph of a cosine function with transformations. It covers identifying the amplitude, period, phase shift, and vertical shift. The tutorial also demonstrates graphing the function over one period and extending it over a larger interval, using graphing tools for accuracy.

What is the coefficient 'a' in the given cosine function?

• 3

• 5

• 1

• 7

How is the amplitude of a cosine function determined?

• By the coefficient of x

• By the absolute value of 'a'

• By the value of 'b'

• By the phase shift 'd'

What is the period of the function if b = π/2?

• 2π

• 2

• 4

• π

What is the phase shift of the function if d = 3?

• Left 3 units

• Up 3 units

• Down 3 units

• Right 3 units

What is the vertical shift of the function if c = 1?

• Up 1 unit

• Right 1 unit

• Down 1 unit

• Left 1 unit

Where does the graph of the function start after the phase shift?

• x = 5

• x = 3

• x = 1

• x = 0

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

• Maximum, midline, minimum, midline

• Midline, minimum, midline, maximum

• Midline, maximum, midline, minimum

• Minimum, midline, maximum, midline

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

• 4

• 7

• 5

• 6

How can the graph be extended over a larger interval?

• By changing the amplitude

• By adjusting the phase shift

• By copying and pasting the pattern

• By altering the vertical shift

Which tool is recommended for graphing the cosine function?

• A tool for quadratic functions

• A tool for linear functions

• A tool for cosine functions

• A tool for sine functions