Question 1: Calculate the value of y when x = 2 in the function y = x³.

Answer: 8

Question 2: Plot the point where x = -3 on the grid for the graph y = x³.

Answer: (−3,−27)

Question 3: Fill in the table for values of y = x³ when x = −1, 0, 1, 2.

Answer: (-1,0,1,8)

Question 4: Construct the graph of y = x³ for x values from -3 to 3. Use the grid to draw the curve smoothly.

Answer: Curve passing through points (-3,-27), (-2,-8), (-1,-1), (0,0), (1,1), (2,8), (3,27)

Question 5: Identify the key features of the graph of y = x³ such as intercepts and symmetry.

Answer: Origin as point (0,0), symmetric about origin

Question 6: Calculate y when x = 4.

Answer: 64

Question 7: What is the value of x when y = 27?

Answer: 3 or -3

Question 8: A student claims that the graph of y = x³ always passes through the point (1,1). Is this true? Explain your reasoning.

Answer: Yes, because for x=1, y=1³=1, so the point (1,1) is always on the graph.

Question 9: Plot the points for x = -2, -1, 0, 1, 2 and draw the cubic curve.

Answer: Points: (-2,-8), (-1,-1), (0,0), (1,1), (2,8)

Question 10: Identify a common mistake students might make when calculating y for x = -2 and explain how to correct it.

Answer: Mistake: calculating y = 2² instead of (-2)³. Correction: cube the negative number: (-2)³ = -8.

Question 11: Challenge: Find the x-value where y = 125 on the graph y = x³.

Answer: 5

Question 12: Extended: If y = x³, what is the value of x when y = -64?

Answer: -4 or 4