Question

F(x)=x^3 -3x^2 +2

Horizontal stretch by a factor of 3 and a translation 3 units up followed by a reflections in the x axis

Answer 1

The equation of the transformed function is j(x) = -x³/27 + x²/3 - 5

How to determine the equation of the transformed function

From the question, we have the following parameters that can be used in our computation:

f(x) = x³ - 3x² + 2

A horizontal stretch by a factor of 3 is represented as

(x, y) = (x/3, y)

So, we have

g(x) = (x/3)³ - 3(x/3)² + 2

g(x) = x³/27 - x²/3 + 2

A translation 3 units up is represented as

(x, y) = (x, y + 3)

So, we have

h(x) = x³/27 - x²/3 + 2 + 3

h(x) = x³/27 - x²/3 + 5

A reflection in the x axis is

(x, y) = (x, -y)

So, we have

j(x) = -x³/27 + x²/3 - 5

Hence, the equation is j(x) = -x³/27 + x²/3 - 5