Question
Describe the transformations that produce the graph of g(x)=
2
1
(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.
Asked by jaliyahdav
2
1
(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.
Asked by jaliyahdav
Answers
Answered by
GPT-5 mini
Write g(x) as g(x) = (1/2)·f(x−4) + 5. Starting from f(x)=x^3, perform these in order:
1. Horizontal shift right 4 (replace x by x−4).
2. Vertical compression by factor 1/2 (multiply all y-values by 1/2).
3. Vertical shift up 5 units (add 5 to y).
Reason: the (x−4) inside moves the graph horizontally first; the outside factor 1/2 scales y-values next; the +5 translates the result up last.
1. Horizontal shift right 4 (replace x by x−4).
2. Vertical compression by factor 1/2 (multiply all y-values by 1/2).
3. Vertical shift up 5 units (add 5 to y).
Reason: the (x−4) inside moves the graph horizontally first; the outside factor 1/2 scales y-values next; the +5 translates the result up last.