describe the transformations that produce the graph of g(x)=1/2(x-4)^3+5 from the graph of the parent function f(x)=x^3. Give the order in which they must be performed to obtain the correct graph

Answer 1

The transformations that produce the graph of g(x) = 1/2(x-4)^3 + 5 from the parent function f(x) = x^3 are:

1. Reflection: Multiply f(x) by -1, resulting in -f(x).
2. Horizontal translation: Shift f(x) 4 units to the right, resulting in f(x-4).
3. Vertical stretch/compression: Compress f(x-4) vertically by a factor of 1/2, resulting in (1/2)(f(x-4)).
4. Vertical translation: Shift (1/2)(f(x-4)) 5 units up, resulting in (1/2)(f(x-4)) + 5.

The correct order in which these transformations must be performed is:

1. Reflection: Multiply f(x) by -1, resulting in -f(x).
2. Horizontal translation: Shift -f(x) 4 units to the right, resulting in -f(x-4).
3. Vertical stretch/compression: Compress -f(x-4) vertically by a factor of 1/2, resulting in (1/2)(-f(x-4)).
4. Vertical translation: Shift (1/2)(-f(x-4)) 5 units up, resulting in (1/2)(-f(x-4)) + 5.

Therefore, the correct order is reflection, horizontal translation, vertical stretch/compression, and vertical translation.