Exploring Translations and Reflections in Geometry

This video tutorial covers the translation and reflection of trigonometric functions, focusing on sine and cosine. It explains how to perform horizontal and vertical translations, also known as phase shifts, and how to graph these functions with transformations. The tutorial further explores vertical and horizontal reflections and demonstrates how to combine these transformations to graph trigonometric functions effectively.

What does a positive value of 'c' in a trigonometric function indicate about its horizontal translation?

• Translation to the right

• Translation to the left

• Vertical translation

• No translation

What is the result of a horizontal translation known as in trigonometric functions?

• Amplitude shift

• Phase shift

• Vertical shift

• Period shift

If 'd' is negative in a trigonometric function, what direction is the vertical translation?

• To the right

• No translation

• Downwards

• Upwards

What is the effect of adding pi/3 to x inside a trigonometric function?

• Shift right by pi/3

• Shift left by pi/3

• No shift

• Vertical shift by pi/3

What does a phase shift to the left by pi/4 indicate about the function's graph?

• It moves right by pi/4

• It moves left by pi/4

• It moves up by pi/4

• It moves down by pi/4

What does a negative 'd' value signify in a trigonometric function's vertical translation?

• Move to the left

• No movement

• Move downwards

• Move upwards

How do you determine the new midline after a vertical shift down by three units?

• No change to the midline

• Move the midline down by three

• Shift the midline left by three

• Move the midline up by three

How does a negative coefficient outside the trigonometric function affect the graph?

• Horizontal reflection

• Vertical reflection

• No reflection

• Shift to the right

What does a vertical reflection involve in terms of point movement on the graph?

• Points above the x-axis move below

• Points below the x-axis move above

• Both A and B

• No movement of points

When combining transformations, what should be adjusted first on the graph?

• Phase shifts

• Reflections

• Horizontal shifts

• Vertical shifts