Question

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

We have been given a parent function $f(x)=x^{3}$ and we need to transform this function into $g(x)=\frac{1}{2}(x-4)^{3}+5$.

We will be required to use three transformations to obtain the required function from $f(x)=x^{3}$.

First transformation would be to shift the graph to the right by 4 units. Upon using this transformation, the function will change to $g(x)=(x-4)^{3}$.

Second transformation would be to compress the graph vertically by half. Upon using the second transformation, the new function becomes $g(x)=\frac{1}{2}(x-4)^{3}$.

Third transformation would be to shift the graph upwards by 5 units. Upon using this last transformation, we get the new function as $g(x)=\frac{1}{2}(x-4)^{3}+5$.