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What is the equation of y = x3
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 is y = x^3.
Vertical stretch by a factor of 3:
This means we multiply the entire equation by 3:
3y = 3x^3.
Horizontal shift 4 units to the right:
To shift the graph 4 units to the right, we replace x with (x - 4):
3y = 3(x - 4)^3.
Vertical shift 3 units down:
To shift the graph 3 units down, we subtract 3 from y:
3(y - 3) = 3(x - 4)^3.
Therefore, the equation of y = x^3 with the given transformations is:
3(y - 3) = 3(x - 4)^3.