• Support PF! Buy your school textbooks, materials and every day products Here!

Transformation Matrices

  • Thread starter exis
  • Start date
  • #1
22
0
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

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,795
925
If you are taking an exam in these, surely you must know something! What have you tried?
 
  • #3
22
0
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)
 
  • #4
22
0
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
 
  • #5
33,182
4,860
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.
 
  • #6
22
0
Ok. I completely got it now. Thanks a lot for your help
 
  • #7
33,182
4,860
And BTW, this has nothing to do with transformation matrices, which you used as the title for this thread.
 
  • #8
22
0
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
 

Related Threads for: Transformation Matrices

  • Last Post
Replies
4
Views
1K
Replies
1
Views
3K
Replies
3
Views
2K
Replies
4
Views
4K
Replies
13
Views
761
  • Last Post
Replies
13
Views
2K
  • Last Post
Replies
3
Views
990
Top