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

Question

The curve whose equation is $y = x^3 + 3$ undergoes, in succession the following transformations: Translation by $4$ units in the negative $x$ direction. Scaling by a scale factor of $2$ parallel to the $x$-axis. Reflection about the $y$-axis. Transformation of the function $y = \mathrm{f}(|x|)$ Find the equation of the resulting curve.

Accepted Answer

$y=\left(4-\frac{|x|}{2}\right)^3+3$

Transformations of Graphs - Composite Transformations

Transformations of Graphs - Composite Transformations

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