Graphing Sine with Period Change and Reflection

The video tutorial explains how to graph the function F(x) = -1/2 sin(x/2). It covers key concepts such as amplitude, period, and critical points. The tutorial demonstrates how to calculate these values and graph the function, including transformations like reflection over the x-axis. The process involves understanding the function's amplitude, determining the period, identifying critical points, and graphing one complete cycle. The video concludes with a demonstration of graphing two complete periods.

What is the amplitude of the function F(x) = -1/2 * sin(x/2)?

• 1

• 1/2

• -1/2

• 2

How do you calculate the period of a sine function?

• π/A

• π/B

• 2π/B

• 2π/A

What is the period of the function F(x) = -1/2 * sin(x/2)?

• 2π

• 4π

• π

• 1/2π

What is the distance between critical points for the function F(x) = -1/2 * sin(x/2)?

• 2π

• π

• π/2

• 4π

What transformation occurs due to the negative sign in the function F(x) = -1/2 * sin(x/2)?

• Reflection over the y-axis

• Horizontal shift

• Vertical stretch

• Reflection over the x-axis

How does the amplitude affect the graph of the function F(x) = -1/2 * sin(x/2)?

• It changes the period

• It changes the reflection

• It changes the vertical stretch

• It changes the horizontal shift

What is the range of the function F(x) = -1/2 * sin(x/2) after considering the amplitude?

• [-π, π]

• [-2, 2]

• [-1/2, 1/2]

• [-1, 1]