The curve whose equation is $y=x^3+2$ undergoes, in succession, the following transformations: A:

Question

The curve whose equation is $y=x^3+2$ undergoes, in succession, the following transformations: A: Translation by $3$ units in the positive $x$-direction. B: Scaling by a scale factor of $2$ parallel to the $x$-axis. C: Translation by $4$ units in the negative $y$-direction. D: Scaling by a scale factor of $3$ parallel to the $y$-axis. Find the equation of the resulting curve.[5]

Accepted Answer

$y=3\left(\frac{x}{2}-3\right)^3-6$

Successive transformations of a cubic curve

Successive transformations of a cubic curve

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