Question

Describe all of the transformations occurring as the parent function f(x) = x^3 is transformed into g(x) = -0.5(3(x+4))^3 -8

Answer 1

Step-by-step explanation:

The translations of the typical functions are

$y = a(bx + c) + d$

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.

• Reflect about the x axis
• Vertical Shrink by a factor of 1/2
• Horizontal Shrink by a factor of 3
• Shift to the left 4 units
• Shift downward 8 units.