Question 1: Calculate y when x = 2 for the function y = x³.

Answer: 8

Question 2: Plot the point corresponding to x = -3 on the graph of y = x³.

Answer: (-3, -27)

Question 3: What is the value of y when x = 0?

Answer: 0

Question 1: Determine the value of y when x = 4.

Answer: 64

Question 2: Plot the point for x = 1 and y = x³ on the grid.

Answer: (1, 1)

Question 3: Find y when x = -2.

Answer: -8

Question 4: Calculate y for x = 3.

Answer: 27

Question 1: A sound wave's intensity is modeled by the cubic function y = x³, where x represents the time in seconds. If at 2 seconds, the intensity is 8 units, what is the intensity at x = -2 seconds? Explain your reasoning.

Answer: The intensity at x = -2 is -8 units because y = (-2)³ = -8. The cubic function is odd, meaning y changes sign symmetrically.

Question 2: A musician adjusts the volume of a sound so that the volume follows y = x³. If the volume at 1 second is 1, what should the volume be at 3 seconds?

Answer: 27

Question 3: If a sound's loudness increases according to y = x³, how much louder is it at x = 4 seconds compared to x = 1 second?

Answer: 64 - 1 = 63 units

Question 1: Plot the points for x = -2, -1, 0, 1, 2 on the graph of y = x³ and describe the symmetry of the graph.

Answer: Points: (-2, -8), (-1, -1), (0, 0), (1, 1), (2, 8). The graph is symmetric about the origin, showing odd symmetry.

Question 2: A sound engineer models the loudness with y = x³, where x is the frequency in kHz. If the loudness at 0.5 kHz is 0.125, what is the loudness at 2 kHz?

Answer: 8

Question 1: A student calculates y = (-3)³ as 9. Explain the mistake and provide the correct answer.

Answer: The mistake is cubing correctly: (-3)³ = -27, not 9.

Question 2: A student plots the point (2, 4) on y = x³, claiming it's correct. Is this right? Why or why not?

Answer: No, because y = x³; for x=2, y=8, not 4. The point should be (2,8).