Graphing cubics, "unsimplified formula" ?

[Kaleidoscope]

Hello, Free Math Help forums! I hope I'm posting in the right section. I am taking a High School-level Pre-Calculus course.
I took some early-level calculus in 2007, but didn't continue and subsequently have forgotten much of what I'd learned then. To refresh myself, I have decided to take a grade 12 Pre-Calculus, but I'm having a bit of trouble getting myself back into everything! I don't want to go back farther than this, and I'm sure that once I get into the swing of things this will all be a breeze, but for the moment I'm a little bit tripped up over a cubic function question.

The question is thus:
If f(x) = x^3 + 3x^2 - x + 6, write an unsimplified formula for
a) g(x) which has the same graph as f(x) moved 2 units to the left
b) h(x) which has the same graph as f(x) moved 3 units down

Now, as far as moving it three units down, I'm fairly confident that this would just be changing the 6 for a 3. Moving the graph horizontally, though, I'm less confident in. I'm also not sure what is meant by "unsimplified formula," is the cubic in something other than a "simplified formula" already?

I'm also not really sure, anymore, about factoring cubics. Looking at that thing, I don't think that I can do any meaningful factoring to it, but I could be wrong?


Thank you so much for your time

 

[BigGlenntheHeavy]

\(\displaystyle f(x) \ = \ x^3+3x^2-x+6\)

\(\displaystyle g(x) \ = \ (x+2)^3+3(x+2)^2-(x+2)+6 \ = \ x^3+9x^2+23x+24\)

\(\displaystyle h(x) \ = \ x^3+3x^2-x+3\)

\(\displaystyle See \ graph, \ can \ you \ tell \ which \ is \ which?\)

[attachment=0:2ls736ra]fff.jpg[/attachment:2ls736ra]

 

[Denis]

If f(x) = x^3 + 3x^2 - x + 6, write an unsimplified formula for.......

"unsimplified" means "complicated" :wink: