Amplitude and Graph Transformations

The video tutorial explains the concept of amplitude, particularly in the context of sine and cosine functions. It begins with an introduction to amplitude, relating it to music and math. The tutorial then defines amplitude as the half distance between the maximum and minimum values of a graph. It demonstrates how to graph sine and cosine functions to determine amplitude, emphasizing the importance of the coefficient 'a' in the function form. The video concludes with examples and a summary of key points.

What is the significance of amplitude in music and mathematics?

• It only applies to musical instruments.

• It connects sound waves to mathematical functions.

• It is unrelated to both fields.

• It determines the pitch of a sound.

How is amplitude defined in the context of a graph?

• The distance from the origin to the minimum value.

• The distance from the origin to the maximum value.

• The half distance between the minimum and maximum values.

• The total distance from the minimum to the maximum value.

What is the amplitude of a sine or cosine function with a maximum value of 1 and a minimum value of -1?

• 2

• 0.5

• 1

• 0

In the standard form of a sine function, y = a * sin(bx - c) + d, what does 'a' represent?

• The frequency of the function.

• The phase shift of the function.

• The vertical shift of the function.

• The amplitude of the function.

If a sine function is given by y = 1/4 * sin(x), what is its amplitude?

• 0

• 1

• 4

• 1/4

What is the amplitude of the function y = -8 * cos(x)?

• -8

• 0

• 8

• 1

How does a negative coefficient affect the graph of a sine or cosine function?

• It changes the amplitude.

• It reflects the graph across the x-axis.

• It shifts the graph vertically.

• It has no effect on the graph.

What is the amplitude of the parent sine and cosine functions?

• 0.5

• 2

• 1

• 0

Why is the amplitude always a positive value?

• Because it is the product of maximum and minimum values.

• Because it is the absolute value of the coefficient.

• Because it is the sum of maximum and minimum values.

• Because it is the distance from the origin.

What happens to the amplitude if the coefficient 'a' is negative?

• The amplitude doubles.

• The amplitude becomes zero.

• The amplitude remains positive.

• The amplitude becomes negative.