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.

(show work)

y = 3 (x - 4) ^3 - 3

Step-by-step explanation:

The sorts of transformations we're usually concerned with involve multiplying the variables by some number or adding some number to them. Each of these four operations has its specific effect.

Here, we're concerned with three of those effects. For an original function f (x), we can write the transformed function g (x) as ...

g (x) = a·f (x-b) + c

The multiplying factor "a" is the vertical stretch factor. The subtracted amount "b" is the horizontal shift to the right. The added amount "c" is the vertical shift upward.

Based on the problem statement, we want a=3, b=4, c=-3. Then our function becomes ...

y = 3 (x - 4) ^3 - 3