Question

The point of inflection of the cubic function f(x)
is (−5,0)
. What is the equation of the new function h(x)
that is obtained by shifting f(x)
6 units to the right?(1 point)
Responses

h(x)=(x−1)3
h left parenthesis x right parenthesis equals left parenthesis x minus 1 right parenthesi cubed

h(x)=(x+11)3
h left parenthesis x right parenthesis equals left parenthesis x minus 1 right parenthesi cubed

h(x)=(x+1)3
h left parenthesis x right parenthesis equals left parenthesis x plus 1 right parenthesi cubed

h(x)=(x−11)3
h left parenthesis x right parenthesis equals left parenthesis x minus 11 right parenthesi cubed

Answer 1

h(x) = (x − 1)^3

Reason: f has inflection at (−5,0), so f(x) is of form (x+5)^3 (up to a constant factor). Shifting right 6 gives h(x)=f(x−6) = ((x−6)+5)^3 = (x−1)^3.