Transformations of Trigonometric Functions

The video tutorial demonstrates how to graph the function 2cos(x-pi/2)+1 by breaking down the process into manageable steps. It starts with sketching the basic cosine graph, then applies a phase shift, changes the amplitude, and finally adds a vertical shift. The instructor explains each transformation step-by-step, ensuring a clear understanding of how each component affects the graph. The tutorial concludes with a complete graph of the function, highlighting the thought process behind each transformation.

What is the function being graphed in this video?

• 2 cosine of (x + π/2) + 1

• cosine of (x - π/2) + 1

• 2 cosine of (x - π/2) + 1

• 2 sine of (x - π/2) + 1

What is the value of cosine(0)?

• 1

• -1

• 2

• 0

At which point does the basic cosine graph return to 1?

• π

• 2π

• π/2

• 3π/2

What does a negative phase shift indicate?

• Shift to the left

• Vertical shift

• Shift to the right

• No shift

What is the first transformation applied to the graph?

• No transformation

• Phase shift

• Amplitude change

• Vertical shift

How does the amplitude change affect the graph?

• It shifts the graph vertically

• It changes the period

• It stretches or compresses the graph vertically

• It shifts the graph horizontally

What is the new amplitude after the transformation?

• -1

• 2

• -2

• 1

What is the second transformation applied to the graph?

• Amplitude change

• Vertical shift

• No transformation

• Phase shift

What happens to the graph when you apply a phase shift and amplitude change together?

• The graph only shifts horizontally

• The graph remains unchanged

• The graph shifts horizontally and stretches or compresses vertically

• The graph shifts vertically

What does the vertical shift do to the graph?

• It changes the period

• It changes the amplitude

• It moves the graph up or down

• It shifts the graph horizontally