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

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(52786)   (Show Source): You can put this solution on YOUR website!
.

g(x) = -f(x-2).             ANSWER

Solved.

Answer by math_tutor2020(3817)   (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.

RELATED QUESTIONS
1.) The function g is related to one of the parent functions g(x) = x^2 + 6 The parent (answered by ikleyn)
find the domain of the composite function f time g. Write the domain in interval... (answered by lwsshak3)
Given the parent function f (x) = |x|, describe the translation of the function g(x) =... (answered by Fombitz)
What is the domain of the composite function f(g(x)) where {{{f(x)=2/(x+10)}}} and... (answered by stanbon)
Write the domain (in interval notation) of the following function: a) f(x) = √x+1 (answered by Fombitz)
For the following function, write a formula in simplest form where {{{ (g*f)(x) }}} , {{{ (answered by Fombitz)
Graph the function of g(x) if h=4 and a=2 and the parent function is f(x)=x^2 Thank... (answered by Fombitz)
Can you please graph the function of g(x) if h=4 and a=2 and the parent function is... (answered by rothauserc)
The function f is defined by f(x) = x^3 Find the expression for g(x) in terms of x in... (answered by swincher4391)