# Transformation Problem

• Nov 21st 2012, 02:17 AM
BobBali
Transformation Problem
Hello All,

Having trouble with below question:

The graph of:
$f(x) = x^3+3x^2-x+4$
is translated to its image g(x) by the vector $\binom{-1}{3}$
Write the new equation of g(x) in the form :
$ax^3+bx^2+cx+d$

Ive tried using the GDC to graph f(x) and then translating points by the vector, but was wondering if there is an algebraic way of doing it without using the GDC? Thanks appreciate it.
• Nov 21st 2012, 09:30 AM
HallsofIvy
Re: Transformation Problem
The old x value is being replaced by x'= x- 1, so that x= x'+ 1, and the old y value is being replaced by y'= y+ 3, so that y= y'- 3:
$y'- 3= (x'+ 1)^3+ 3(x'+ 1)^2- (x'+ 1)+ 4$. Multiply those out and then replace x' with x and y' with y.
• Nov 21st 2012, 11:08 AM
skeeter
Re: Transformation Problem
$g(x) = f(x+1) + 3$