Question 1: Describe the transformation that maps y = x³ to y = (x - 2)³ + 3.

Answer: Horizontal shift right 2, vertical shift up 3

Question 2: Plot the graph of y = (x + 1)³ - 2 on the grid.

Answer: Student plots shifted left 1 and down 2

Question 3: A cubic graph y = x³ is reflected across the x-axis and then translated 4 units to the left. Write the equation of the transformed graph.

Answer: y = - (x + 4)³

Question 4: Construct a cubic graph that is vertically stretched by a factor of 3 and shifted down 2 units. Write the equation of your graph.

Answer: y = 3x³ - 2

Question 5: Identify the sequence of transformations needed to turn y = x³ into y = (x - 1)³ + 4, and describe each step.

Answer: Shift right 1, shift up 4

Question 6: The graph of y = x³ is reflected across the y-axis and stretched vertically by a factor of 2. Write the equation of the resulting graph.

Answer: y = -2x³

Question 7: A cubic graph is translated 3 units down and reflected across the x-axis. What is the equation of this graph?

Answer: y = - (x³ - 3)

Question 8: Explain how the graph y = x³ is affected by the transformation y = - (x - 2)³ + 5.

Answer: Reflected across x-axis, shifted right 2, shifted up 5

Question 9: Plot the graph of y = 0.5x³ + 1 and describe the transformation from y = x³.

Answer: Vertical compression by 0.5, shift up 1

Question 10: A cubic graph undergoes a reflection across the y-axis and a vertical compression by a factor of 2. Write the new equation.

Answer: y = -2x³

Question 11: Identify two common mistakes students make when performing transformations on cubic graphs and explain how to correct them.

Answer: Mistake 1: Confusing translation with reflection - fix by carefully analyzing the transformation sequence. Mistake 2: Forgetting to adjust the sign during reflection - ensure to change the sign of the function appropriately.