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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 find the equation of the transformed function, we'll apply the given transformations to the original function.
The original function is y = x^3.
1. Vertical stretch by a factor of 3:
The equation becomes y = 3x^3 (Multiplied all y-values by 3).
2. Horizontal shift 4 units to the right:
We replace x with (x - 4) in the equation to shift the graph 4 units to the right.
The equation becomes y = 3(x - 4)^3.
3. Vertical shift 3 units down:
We subtract 3 from the equation to shift the graph 3 units down.
The equation becomes y = 3(x - 4)^3 - 3.
So, the equation of y = x^3 with the given transformations is y = 3(x - 4)^3 - 3.