Transformations and Properties of Sine Functions

The video tutorial explains how to graph the function y = 2sin(-x) over the interval [-2π, 2π]. It begins by graphing y = sin(x) and discusses its period and amplitude. The tutorial then scales the function to y = 2sin(x), doubling the amplitude. Next, it reflects the graph to y = sin(-x) over the y-axis. Finally, it combines these transformations to graph y = 2sin(-x), maintaining the period but altering the amplitude and orientation.

What is the initial function we are asked to graph?

• y = 2sin(-x)

• y = sin(x)

• y = cos(x)

• y = 2cos(x)

Tags

CCSS.HSF.TF.A.4

What is the period of the function y = sin(x)?

• 4π

• π/2

• 2π

• π

Tags

CCSS.HSF-IF.C.7E

How does the amplitude change when graphing y = 2sin(x)?

• It halves

• It remains the same

• It doubles

• It triples

Tags

CCSS.HSF-IF.C.7E

What transformation occurs when graphing y = sin(-x)?

• Reflection over the y-axis

• Horizontal shift

• Vertical stretch

• Reflection over the x-axis

Tags

CCSS.HSF-IF.C.7E

What is the effect of the negative sign in y = sin(-x)?

• It reflects the graph over the y-axis

• It shifts the graph vertically

• It changes the period

• It doubles the amplitude

Tags

CCSS.HSF-IF.C.7E

How does the graph of y = 2sin(-x) differ from y = 2sin(x)?

• It has a different period

• It is reflected over the x-axis

• It has a different amplitude

• It is reflected over the y-axis

Tags

CCSS.HSF.TF.A.4

What is the period of the function y = 2sin(-x)?

• π/2

• 4π

• 2π

• π

Tags

CCSS.HSF-IF.C.7E

What happens to the amplitude when graphing y = 2sin(-x)?

• It halves

• It remains the same

• It triples

• It doubles

Tags

CCSS.HSF-IF.C.7E

Which of the following describes the transformation from y = sin(x) to y = 2sin(-x)?

• Vertical stretch and reflection over the x-axis

• Vertical stretch and reflection over the y-axis

• Horizontal shift and reflection over the y-axis

• Horizontal shift and vertical stretch

Tags

CCSS.HSF-IF.C.7E

What is the relationship between the periods of y = sin(x) and y = 2sin(-x)?

• The period of y = 2sin(-x) is half

• The period of y = 2sin(-x) is double

• The period of y = 2sin(-x) is triple

• The periods are the same

Tags

CCSS.HSF-IF.C.7E