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
The original equation of y = x^3 can be transformed into a new equation with the given transformations as follows:
Vertical stretch by a factor of 3: This can be done by multiplying the original function by 3 on the outside of the function, resulting in y = 3x^3.
Horizontal shift 4 units to the right: This can be achieved by replacing x with (x - 4) inside the function, resulting in y = 3(x - 4)^3.
Vertical shift 3 units down: This can be achieved by subtracting 3 from the function, resulting in y = 3(x - 4)^3 - 3.
Therefore, the final equation of y = x^3 with the given transformations is y = 3(x - 4)^3 - 3.