# Transformation Matrices

Hi

I'm sitting for an AQA exam tomorrow (Pure Maths MPC2) and while going through some past papers I encountered this problem which I'm not sure how to solve. I'd appreciate any help :)

## Homework Statement

i) Describe a single geometrical transformation that maps the graph of y=6^x onto the graph of y=6^(3x).

ii) The graph of y=6^x is translated by the matrix [1; -2] (it is a 2x1 matrix) to give the graph of the curve with equation y=f(x) . Write down an expression for f(x).

## Answers and Replies

HallsofIvy
Science Advisor
Homework Helper
If you are taking an exam in these, surely you must know something! What have you tried?

well, if i were doing the exam right now, for i) i'd say it would compress the x-axis
however i'm pretty uncertain about (ii)

while thinking about the second part I came up with two possible solutions which both seem right and ended up getting more confused

you shift every (x,y) points by the vector [1 -2] (ie move one to the right and down two)
or
use the matrix transformation equation and end up with y=x-2*6^x

Mark44
Mentor
ii) The graph of y=6^x is translated by the matrix [1; -2] (it is a 2x1 matrix) to give the graph of the curve with equation y=f(x) . Write down an expression for f(x).

After some thought, I think what this means is that each point on the graph of y = 6^x is translated one unit right and two units down. The description is a bit confusing in its description of the graph being translated by a matrix. Although [1 -2]^T is indeed a matrix, it might have been clearer to describe this as a translation by an amount represented by the given vector.

Ok. I completely got it now. Thanks a lot for your help

Mark44
Mentor
And BTW, this has nothing to do with transformation matrices, which you used as the title for this thread.

Sorry about that. At the time I posted the problem I still thought that I needed to use the matrix transformation equation to solve it. The wording of the question confused me