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
To determine the equation of the transformed function, we will apply each transformation step by step to the original function y = x^3.
1. Vertical stretch by a factor of 3:
To vertically stretch the function by a factor of 3, we multiply the entire function by 3. So the function becomes y = 3(x^3).
2. Horizontal shift 4 units to the right:
To shift the function 4 units to the right, we replace the variable x with (x - 4). Thus, the function becomes y = 3((x - 4)^3).
3. Vertical shift 3 units down:
To shift the function 3 units down, we subtract 3 from the function. Thus, the final transformed equation becomes y = 3((x - 4)^3) - 3.