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cricket20 [7]
3 years ago
14

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 th

e order in which they must be performed to obtain the correct graph
Mathematics
1 answer:
SSSSS [86.1K]3 years ago
6 0

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.

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