4e Example 1 Part 2 (How to graph the Cosine Functions)

The video tutorial covers transformations of the cosine function, including amplitude, period, phase shift, and vertical shift. It explains how to graph these transformations and discusses reflections about the axes and the range of the cosine graph. The tutorial also covers phase shift and period adjustments, as well as double reflections and vertical shifts. Finally, it introduces the tangent graph and its transformations.

What is the amplitude of a cosine function with an amplitude of 1?

• 0

• 3

• 1

• 2

If a cosine graph is shifted π/4 to the right, what is the phase shift?

• π/4 to the left

• π/4 to the right

• π/2 to the right

• π/2 to the left

What is the new range of a cosine function shifted up by 1 unit?

• -2 to 0

• 1 to 3

• 0 to 2

• -1 to 1

How does a vertical shift of 1 unit affect the cosine graph?

• Compresses the graph

• Stretches the graph

• Shifts the graph up

• Shifts the graph down

What happens to a cosine graph when it is reflected about the X-axis?

• It flips vertically

• It shifts up

• It flips horizontally

• It shifts down

What is the period of a cosine function with B = 1/4?

• 2π

• 4π

• 8π

• π

How does a fractional amplitude affect the cosine graph?

• Increases the period

• Decreases the period

• Changes the amplitude

• Changes the phase shift

What is the phase shift of a cosine function with a phase shift of π units to the right?

• 2π units to the left

• 2π units to the right

• π units to the right

• π units to the left

What is the effect of reflecting a cosine graph about the Y-axis?

• Flips vertically

• Flips horizontally

• Shifts up

• No change

What is the range of a cosine function shifted down by 2 units?

• 0 to 2

• -1 to 1

• -3 to -1

• 1 to 3