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

Answer: 8

Question 2: Plot the point on the grid where x = -3 and find the corresponding y value.

Answer: -27

Question 3: Determine the value of y when x = -1.

Answer: -1

Question 4: What is the y-coordinate when x = 0?

Answer: 0

Question 5: Sketch the graph of y = x³ for x values from -3 to 3. Use the grid to plot points and connect smoothly.

Answer: Plot points at (-3, -27), (-2, -8), (-1, -1), (0, 0), (1, 1), (2, 8), (3, 27).

Question 6: Identify the pattern in the y-values for x = -2, -1, 0, 1, 2. Describe the pattern and predict y when x = 4.

Answer: The y-values are cubes of x, so -8, -1, 0, 1, 8. For x=4, y=64.

Question 7: If a point (x, y) lies on the graph of y = x³ and x = 5, what is y?

Answer: 125

Question 8: Construct a cubic curve through the points (−2, −8), (0, 0), and (2, 8). Do these points lie on y = x³?

Answer: Yes, all these points satisfy y = x³ because (-2)^3 = -8, (0)^3=0, (2)^3=8.

Question 9: Identify the error in the following statement: 'Y = (x + 1)^3 gives the same shape as y = x^3 but shifted left by 1 unit.'

Answer: The statement is correct; (x+1)^3 shifts the graph left by 1 unit.

Question 10: Predict the y-value for x = -4 and explain the pattern.

Answer: -64

Question 11: Challenge: Without graphing, determine the approximate x-value where y = 64. Explain your reasoning.

Answer: x ≈ 4 because 4^3 = 64.