Question

I'm begging for help here. f(x)=x^3-2x^2+3x and g(x)=3f(x+2)-1 List the transformations of f(x) to g(x) and obtain an algebraic representation of g(x).
I am pretty sure the answer is shifting 2 units left, 1 unit up, and stretching vertically by 3. My possible answer for the second part is g(x)=3x^3-6x^2+9x+17. Can anyone tell me if I'm in the right direction?

Answer 1

g(x)=3f(x+2)-1
=3[(x+2)^3-2(x+2)^2+3(x+2)] -1
=3[(x+2)^2(x+2-2)+3x+6] -1
=3[(x+2)^2(x)+3x+6] -1
=3[x(x+2)^2+3x+6] -1
=3[x(x^2+4x+4)+3x+6] -1
=3[x^3+4x^2+4x+3x+6] -1
=3[x^3+4x^2+7x+6] -1
=[x^3+12x^2+21x+18] -1
=x^3+12x^2+21x+17

Answer 2

shanna please help me here? I'm sorry but I'm not really sure what you did as far as your distribution. I have the same first line as you, but afterwards I got lost