Graph a sine Function with a Horizontal Translation

The video tutorial explains the properties of the sine graph, including its period, amplitude, and key points like X intercepts, minimum, and maximum. It discusses how the graph remains unchanged when amplitude and period are not altered. The tutorial then focuses on horizontal translations, explaining how to determine new endpoints by setting the function equal to 0 and 2π. An example is provided to illustrate shifting the graph π units to the right. The tutorial concludes by summarizing the process of graph transformations, emphasizing the importance of understanding horizontal translations.

What is the period of a standard sine function?

• 3π

• π/2

• π

• 2π

What is the maximum value of a standard sine function?

• -1

• 1

• 0

• 2

In a sine function, what does the term 'amplitude' refer to?

• The maximum height from the centerline

• The horizontal shift of the graph

• The vertical shift of the graph

• The distance between two consecutive peaks

How do you determine the new endpoints of a sine graph after a horizontal translation?

• By subtracting a constant from the original endpoints

• By multiplying the original endpoints by a constant

• By setting the function's expression equal to the original endpoints and solving

• By adding a constant to the original endpoints

If a sine graph is shifted π units to the right, what happens to its starting point?

• It remains the same

• It shifts π units to the right

• It shifts π units to the left

• It shifts 2π units to the right