Transformations of Sine and Cosine Functions

The video tutorial covers translating sine and cosine functions, focusing on horizontal and vertical shifts, known as phase and vertical shifts, respectively. It explains how to apply these translations to sine and cosine functions, providing examples and graphing techniques. The tutorial also discusses combining multiple transformations into one equation and writing equations to model translations.

What is the primary focus when translating sine and cosine functions?

• Modifying the function's domain

• Translating the function horizontally and vertically

• Adjusting the function's frequency

• Changing the function's amplitude

What is a phase shift in the context of periodic functions?

• A vertical shift of the function

• A change in the function's amplitude

• A horizontal shift inside the function

• A modification of the function's period

In the equation y = a * sin(bx - h) + k, what does 'a' represent?

• The period

• The vertical shift

• The phase shift

• The amplitude

How does a negative sign in front of the amplitude affect the sine function?

• It changes the function's period

• It reflects the function over the x-axis

• It shifts the function vertically

• It modifies the function's phase shift

What is the effect of a horizontal shift of f(x - h) on the graph of a sine function?

• The graph shifts h units to the left

• The graph shifts h units to the right

• The graph shifts h units upward

• The graph shifts h units downward

In the equation y = cos(x - π) + 5, what is the vertical shift?

• 5 units down

• π units to the right

• 5 units up

• π units to the left

When combining transformations, what is the first step in graphing the function?

• Identify the amplitude

• Plot the reference graph

• Calculate the period

• Determine the phase shift

How do you write an equation for a cosine function that is shifted up by 3 units?

• y = cos(x) + 3

• y = cos(x) - 3

• y = cos(x + 3)

• y = cos(x - 3)