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
To obtain the graph of g(x)=1/2(x-4)^3+5 from the parent function f(x)=x^3, you must perform the transformations in the following order:
1. Horizontal translation to the right by 4 units: (x-4)
This shifts the graph 4 units to the right.
2. Vertical stretch by a factor of 1/2: 1/2(x-4)^3
This compresses the graph vertically by a factor of 1/2.
3. Vertical shift upward by 5 units: 1/2(x-4)^3+5
This shifts the graph 5 units upwards.
The correct order of transformations is therefore:
1. Horizontal translation to the right by 4 units: (x-4)
2. Vertical stretch by a factor of 1/2: 1/2(x-4)^3
3. Vertical shift upward by 5 units: 1/2(x-4)^3+5