Question:
What is the equation of y = x 3 with the given transformations? vertical stretch by a factor of 3, horizontal shift 4 units to the right, vertical shift 3 units down.
Answers:
(1) y = 3(x - 4)³ - 3
(2) y = 3(x - 4)^3 - 3
Step-by-step explanations:
(1) The parent function is y = x³.
After a vertical stretch by a factor of 3, obtain
y = 3x³
After a horizontal shift 4 unit to the right, obtain
y = 3(x - 4)³
After a vertical shift 3 units down, obtain
y = 3(x - 4)³ - 3
(2) A vertical stretch factor 3 is given by 3x^3. Horizontal shift 4 to the right is given by 3(x - 4)^3. Finally we add -3 to this function to move it 3 units down.
Answer is y = 3(x- 4)^3 - 3
