Graphing the Sine Function with a Vertical Shift

The video tutorial explains how to graph a trigonometric function with transformations. It covers determining amplitude, period, critical points, and start/end points. The tutorial also discusses graphing with transformations, including reflections and vertical shifts, to achieve the final graph.

What is the amplitude of the function 2 - sin(2πx/3)?

• 1

• 3

• 2

• -1

How do you calculate the period of a trigonometric function?

• The sum of the coefficients

• The reciprocal of the amplitude

• The absolute value of the amplitude

• 2π divided by the coefficient of x

What is the distance between the critical points if the period is 3?

• 4

• 1

• 3/4

• 3

What are the start and end points of the graph for the function 2 - sin(2πx/3)?

• π and 2π

• 0 and π

• 0 and 3

• 0 and 2π

What effect does a positive transformation outside the function have on the graph?

• Shifts the graph down

• Reflects the graph over the y-axis

• Shifts the graph up

• Reflects the graph over the x-axis

How does a reflection about the x-axis affect the sine graph?

• It shifts the graph up

• It shifts the graph down

• It inverts the graph

• It stretches the graph

What is the final step in graphing a function with a vertical transformation?

• Multiply each point by the transformation value

• Subtract the transformation value from each point

• Divide each point by the transformation value

• Add the transformation value to each point