The function f(x)=x^3 undergoes a transformation such that 3f(x+2)^3 =3(x+2)^3 (2 points) This translates the graph horizontally to the ?Left/Right and then stretched ?horizontally/vertically

Answer 1

Let's analyze the transformation for the function \( f(x) = x^3 \).

1. Horizontal Transformation:

   • The function \( f(x+2) \) indicates a horizontal translation.
   • Since we have \( x+2 \), the graph of \( f(x) \) shifts to the left by 2 units. This is because adding a positive value inside the function argument (\( x+2 \)) moves the graph left.

2. Vertical Transformation:

   • The expression \( 3f(x+2)^3 \) means you are taking the output of \( f(x+2) \) and cubing it, which does not change the vertical stretch. However, the factor of 3 in front of \( f(x+2) \) vertically stretches the graph by a factor of 3.

In summary, the graph of \( f(x) = x^3 \) is:

• Translated horizontally to the left by 2 units.
• Stretched vertically by a factor of 3.

So the complete answer is: left and vertically.