Transformations of Sine Functions

In this video, Anil Kumar explains how to sketch the graph of a transformed trigonometric function. The function is given as f(x) = 2sin(0.5x - π/4) + 1. The video covers factoring the function to understand horizontal translation, calculating the time period and amplitude, and sketching the graph in steps. An alternate method using a table of values is also discussed to help visualize the transformation and graph the function accurately.

What is the initial function given in the video?

• f(x) = 2 sin(x/2) - π/4 + y

• f(x) = 2 sin(x) - π/4 + y

• f(x) = sin(2x - π/4) + y

• f(x) = 2 sin(1/2 x - π/4) + y

What is the horizontal translation of the function after factoring?

• π/4 to the left

• π/2 to the left

• π/2 to the right

• π/4 to the right

What is the time period of the transformed sine function?

• 8π

• π

• 4π

• 2π

What is the amplitude of the function?

• 3

• 1

• 2

• 4

What is the first step in sketching the function?

• Draw the axis line at y = 1

• Draw the sine wave

• Draw the maximum value line

• Draw the minimum value line

How is the function shifted horizontally?

• By π to the right

• By π/2 to the right

• By π to the left

• By π/2 to the left

What is the end point of the graph after the horizontal shift?

• 5π

• 4π

• 9π/2

• 8π

What is the alternative method to sketch the graph?

• Using a ruler and compass

• Using a calculator

• Using a table of values

• Using a graphing software

How are the x-values transformed in the alternative method?

• Multiplied by 2 and subtracted by π/2

• Divided by 2 and added by π/2

• Multiplied by 2 and added by π/2

• Divided by 2 and subtracted by π/2

How are the y-values transformed in the alternative method?

• Divided by 2 and added by 1

• Multiplied by 2 and added by 1

• Divided by 2 and subtracted by 1

• Multiplied by 2 and subtracted by 1