The perimeter of a rectangle is given by the formula,
We substitute,
and
into the above formula to obtain the expression,
We now group the x and y terms on the Left Hand Side of the equation to get.
We now divide through by 2 to get,
Therefore the width of the rectangle is
Step-by-step explanation:
The translations of the typical functions are
Where a is the vertical translation,
If a is greater than 1 or less than -1, we have a vertical stretch
If a is between -1 and 1 , we have a vertical compressions or shrink.
If a is negative, we have a negative reflection across the x axis.
If b is greater than 1 or less than -1, we have a horizontal compression or shrink
If b is between -1 and 1, we have a horizontal stretch
If b is negative, we have a reflection about the y axis,
If c is negative, we have a translation to the right c units
If c is positive, we have a translation to the left c units
If d is positive, we have a translation upward d units
If d is negative, we have a translation downward d units.
Here in this problem, our parent function is x^3.
So I would do the following transformations.