SOLUTION: g(x)= -(x-2)³ parent function ,f = x³ Write g(x) in terms of f using function notation

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Question 1196873: g(x)= -(x-2)³
parent function ,f = x³
Write g(x) in terms of f using function notation
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52785) About Me  (Show Source):
You can put this solution on YOUR website!
.

g(x) = -f(x-2).             ANSWER


Solved.



Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

f(x) = x^3
f(x-2) = (x-2)^3 ... replace each x with x-2
-f(x-2) = -(x-2)^3 ... multiply both sides by -1
-f(x-2) = g(x)
g(x) = -f(x-2)

The replacement of x with x-2 means the entire curve shifts 2 units right.
The negative out front reflects the curve over the x axis.