:polonymal :

question : find a, b and c.

2x^3 +3x^2 -4x -5 = a(x+1)^3 +b(x+1)^2 +c(x+1)

for explaining

Expand the right hand side, simplify, and match up the coefficients of same-power terms.




Since this must be the same as , you need to satisfy



The solution for is already given, . Substitute this into the second equation to find .



Now plug into either remaining equation to find .



And just to check that the third equation is also satisfied,

Answers: the graph is translated down 1 unit and the domain and range of g(x) is the same as the domain and range of f(x).