Describe the transformations that produce the graph of gx 1

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.

Solution

f(x) = x³

- Translate this function f(x) by 4 units on the x axis. This new function will be: h(x) = (x - 4)³.

- Divide h(x) by 2. This gives k(x) = 1/2 [x - 4]³. This decreases the speed with which the graph is changing values by a factor of 2.

- Translate this function k(x) by 5 units on the y axis. This new function will be: g(x) = 1/2(x - 4)³ + 5.