Graphing a Sine Function with a Transformation

The video tutorial explains how to graph the sine function with a horizontal shift transformation. It begins by identifying the amplitude and period of the sine function, then demonstrates graphing the parent function. The tutorial proceeds to apply a horizontal shift, detailing the process of shifting the entire graph. Key points such as intercepts, maxima, and minima are identified after the transformation. The tutorial emphasizes careful placement of the y-axis and listing important graph parts.

What is the amplitude of a sine function if the absolute value of 'a' is 1?

• 0

• 2

• 3

• 1

How do you determine the period of a sine function?

• π

• 2π

• 2π/b

• b/2π

What is the first step in graphing a sine function with transformations?

• Apply vertical shift

• Graph the parent function

• Find the maximum point

• Determine the intercepts

What is the effect of a horizontal shift of pi/4 on the sine function?

• Shifts the graph down

• Shifts the graph to the left

• Shifts the graph up

• Shifts the graph to the right

When applying a horizontal shift, what should you be cautious about?

• The vertical shift

• The y-axis placement

• The amplitude

• The period

Which point is considered a maximum in the transformed sine graph?

• pi/4, 0

• 3pi/4, 0

• 5pi/4, 0

• 7pi/4, 0

What is the final step in graphing a sine function with transformations?

• List the key points

• Apply vertical shift

• Determine the period

• Find the amplitude