To obtain the graph of g(x) = 1/2 (x-4)^3 +5 from the graph of f(x) = x^3, the following transformations need to be performed in the given order:
1. Horizontal translation: The graph of g(x) is shifted 4 units to the right from the graph of f(x) due to the term (x-4) in the equation. This horizontal translation is performed before any other transformation.
2. Vertical stretch/compression: The graph of g(x) is vertically compressed by a factor of 1/2 from the graph of f(x) due to the coefficient 1/2 multiplying the equation. This transformation is performed after the horizontal translation.
3. Vertical translation: The graph of g(x) is shifted 5 units up from the graph of f(x) due to the term +5 added to the equation. This transformation is performed after the vertical stretch/compression.
Therefore, the correct order of transformations is:
1. Horizontal translation by 4 units to the right.
2. Vertical stretch by a factor of 1/2.
3. Vertical translation by 5 units up.
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.
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