Understanding Cosine Functions and Graphs

This video tutorial explains how to graph a transformation of the cosine function in the form y = a * cos(bx + c) + d. It covers the significance of each parameter: 'a' for amplitude, 'b' for period, 'c' for phase shift, and 'd' for vertical shift. An example is provided to demonstrate the calculation of these transformations and how to graph the resulting function. The video concludes with instructions on completing the graph by repeating the pattern.

What is the amplitude of a cosine function if the absolute value of 'a' is 5?

• 1

• 5

• 10

• 2.5

If 'b' is 4 in the cosine function, what is the period?

• π

• 2π

• 4π

• π/2

What is the phase shift if 'c' is π and 'b' is 2?

• π/2 to the right

• π/2 to the left

• π to the right

• π to the left

How does a negative 'd' value affect the graph of a cosine function?

• Shifts right

• Shifts left

• Shifts down

• Shifts up

Where is the midline of the graph if 'd' is -3?

• y = 1

• y = 0

• y = -3

• y = 3

What is the maximum value of the function if the amplitude is 4 and the midline is y = -2?

• 6

• 2

• 0

• 4

How many sub-intervals are used to graph one period of a cosine function?

• 2

• 3

• 5

• 4

What is the minimum value of the function if the amplitude is 3 and the midline is y = 1?

• 0

• -1

• 1

• -2

How can you extend the graph of a cosine function beyond one period?

• By altering the phase shift

• By repeating the pattern

• By changing the amplitude

• By adjusting the midline

What happens to the graph if you move to the right of one period?

• It reflects

• It ends

• It starts a new period

• It shifts up