Question 1: Given the cubic function y = x^3, find the equation of the shifted graph when moved 3 units to the right and 2 units up.

Answer: y = (x - 3)^3 + 2

Question 2: Plot the graph of y = (x - 1)^3 + 4. What is the new y-value when x=2?

Answer: 5

Question 3: If y = x^3 is reflected across the x-axis, what is the new equation?

Answer: y = -x^3

Question 4: What is the effect of multiplying y by 2 on the graph of y = x^3?

Answer: Vertical stretch by a factor of 2

Question 1: A cubic graph y = x^3 is shifted 2 units left and compressed vertically by a factor of 1/2. Write the new equation and explain the transformation.

Answer: y = (1/2)(x + 2)^3; the graph shifts 2 units left and is compressed vertically by factor of 1/2.

Question 2: A cubic function y = x^3 is reflected and then shifted down 3 units. Write the final equation and describe the transformations.

Answer: y = -x^3 - 3; reflection across x-axis followed by downward shift of 3 units.

Question 3: A cubic function's graph is stretched vertically by a factor of 3 and translated 4 units right. Write the new function.

Answer: y = 3(x - 4)^3

Question 4: Explain the combined effect of shifting y = x^3 five units down and reflecting across the x-axis.

Answer: The transformation results in y = - (x)^3 - 5, reflecting across x-axis and shifting down 5 units.

Question 1: A store offers a cubic pricing model where total cost y (in dollars) for x items is y = 2x^3. If they apply a 10% discount, what is the new cost function? Plot the function for x=1 to 3.

Answer: y = 1.8x^3; students plot for x=1,2,3.

Question 2: A cubic cost function y = 3(x - 2)^3 models the price of a product after a promotional shift. If a customer buys 4 items, what is the total cost? Show your work.

Answer: y = 3(4 - 2)^3 = 3(2)^3 = 24 dollars

Question 3: A store displays cubic price increases based on quantity, with total cost y = x^3 + 5. What is the cost for 5 items, and how does the graph shift if the constant 5 is removed?

Answer: Cost for 5 items: y=125+5=130; removing 5 shifts the graph down by 5 units.

Question 1: Design a cubic transformation that models the effect of a 15% increase in price followed by shifting the price 3 dollars lower. Write the final equation.

Answer: y = 1.15(x)^3 - 3

Question 2: A cubic graph is stretched vertically by 2, shifted 2 units right, and reflected across the y-axis. Write the resulting equation.

Answer: y = -2(x + 2)^3

Question 1: Plot the function y = (x + 2)^3 - 4 on the grid and identify the transformations applied.

Answer: Shift left 2 units, down 4 units.

Question 2: Describe the effect of multiplying y = x^3 by -1 and then adding 7.

Answer: Reflection across x-axis and upward shift of 7 units.

Question 1: A student states: 'To shift y = x^3 three units left, I write y = (x + 3)^3.' Is this correct? Why or why not?

Answer: Yes, it's correct; shifting left 3 units uses (x + 3)^3.

Question 2: A student reflects y = x^3 across the y-axis and writes y = -x^3. Is this accurate? Explain.

Answer: No, reflection across y-axis results in y = -x^3; this is correct for x-axis reflection. For y-axis, it should be y = (-x)^3.