Graphing Sine and Cosine Functions Assignment

The graph models a weight bobbing up and down on a spring. How far does the weight travel, going from maximum displacement to minimum displacement?

4 inches

A group of students uses a rope swing to cross back and forth over a stream. The motion of the students is modeled using a cosine function. What is the amplitude of the function?

8 feet

Which of the following statements are true? Check all that apply.

A. The amplitude is 1/2 D. The graph is compressed horizontally by a factor of 1/2 E. The equation of the graph is Y=1/2 sin(2x)

The function represented by the table has the form y=acos(bx). Which of the following statements are true? Check all that apply.

A. The function increases on the interval (pi, 2pi) C. The frequency is 1/2pi D. The maximum value of the function is 6

Consider the following function: Y=1/4 cos(-1/4 x) Which of the following statements are true? Check all that apply.

A. The graph is symmetric to the y-axis. B. The function decreases on the interval (0, 4pi) E. The graph has x-intercepts at x=2pi and x=6pi

Which graph represents the equation Y=3sin(1/3 x)?

B

Which of the following statements are true? Check all that apply.

B. The graph is stretched vertically by a factor of 5 D. The graph is stretched horizontally by a factor of 2 E. The period is 4pi

Which graph represents a function with amplitude 4 and period pi?

D.

Which domain window settings would be appropriate if you wanted to graph the function below in degrees for exactly 3 periods? Y=4sin(3x)

Xmin=-90 Xmax=270

A cosine function has been reflected over the x-axis and horizontally compressed by a factor of 1/3. Which equation matches this description?

Y=-cos(3x)