How do you map the graph of y=6^x onto the graph of y=6^(3x)?

[exis]

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).

 

[HallsofIvy]

If you are taking an exam in these, surely you must know something! What have you tried?

 

[exis]

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)

 

[exis]

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]

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.

 

[exis]

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

 

[Mark44]

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

 

[exis]

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