Transforming Sinusoidal Functions: Stretching and Shrinking

This lesson covers the transformation of sinusoidal functions, focusing on stretching and shrinking them both horizontally and vertically. It reviews the basic shapes of sine and cosine graphs and explains how to plot them using a five-point pattern. The lesson details how the values of A and B affect the amplitude and period of the graphs, respectively. It also guides students on determining equations from given graphs and sketching graphs from equations, emphasizing the impact of negative values and the importance of scaling axes correctly.

What is the basic shape of the sine curve?

• A circle

• A straight line

• A sideways C starting at the high point

• A sideways S starting on the midline

How does multiplying the function by a value A affect the graph?

• It changes the phase shift

• It changes the amplitude

• It changes the frequency

• It changes the period

What happens to the graph when A is negative?

• The graph shifts to the right

• The graph flips upside down

• The graph becomes a straight line

• The graph shifts to the left

What does the parameter B represent in the transformation of sinusoidal functions?

• The amplitude of the graph

• The phase shift of the graph

• The vertical shift of the graph

• The number of waves completed from 0 to 2π

What is the effect of increasing the absolute value of B on the period of the graph?

• The period decreases

• The period becomes negative

• The period increases

• The period remains the same

If a graph has an amplitude of 3, what is the equation of the sine function?

• y = 3 sin(x)

• y = sin(x) + 3

• y = sin(3x)

• y = 3 + sin(x)

How do you determine the period of a sine function with a given B value?

• Period is B/2π

• Period is 2π/B

• Period is 2πB

• Period is B