Understanding Vector Transformation with <1,-1> Translation - Explained

[kvzrock]

what does it mean by applying vector <-1,-1> to translate f(x) to h(x)?

 

[HallsofIvy]

"Translation" in general means to add a vector. Since you haven't told us what "f(x)" and "h(x)" represent I can't be more specific but if they are vector valued functions, then I would suspect you are to add the vector <-1,-1> to f(x).

 

[kvzrock]

f(x)=x^3-3x^2
h(x) should be in the form of ax^3+bx^2+cx+d

edit: problem solved. Thanks.

 

[HallsofIvy]

I suspect that you are intended to find a function whose graph looks exactly line y= f(x) but is translated (one translates geometric things- points and sets of points like graphs- not functions) by <-1,-1>. In particular, that means that, since f(0)= 0, we want g(-1)= -1. First, we want x= -1, in g, to "act like" x=0 in f. That is
g(x)= f(u) for some u so that when x= -1, u= 0: okay the simplest possible thing is u= x+1. If we write g(x)= f(x+1)= (x+1)³- 3(x+1)², we have g(-1)= f(0) but we are not quite done: g(-1)= f(0)= 0 and we want g(-1)= f(0)-1. Fine: just subtract 1 from what we just got:

g(x)= (x+1)³- 3(x+1)²- 1.

In order to get it in the form "ax³+ b²+ cx+ d", you will need to multiply it out.