How to do this question in regards of matrices and transformation?

enter image source here

1 Answer
Feb 3, 2018

#(y'-4)/2=-2((x'+1)/4)^3+6((x'+1)/4)#

or simplified

#y=-x^3/16-(3x^2)/16+(45x)/16+111/16#

Explanation:

From the matrices, the function is going to be dilated by a factor of 4 from the y-axis, 2 from the x-axis, translated 1 unit to the left and 4 units up.

Do the matrix multiplication first

#AX=((4,0),(0,2))((x),(y))=((4x),(2y))#

Then the addition

#AX+B=((4x),(2y))+((-1),(4))=((4x-1),(2y+4))#

Put it together to get

#X'=AX+B=((4x-1),(2y+4))#

#X'=((x'),(y'))#

#((x'),(y'))=((4x-1),(2y+4))#

Now that we have expressions for x' and y', rearrange them to solve for x and y.

#x'=4x-1rArrx=(x'+1)/4#

#y'=2y+4rArry=(y'-4)/2#

Finally, substitute the expressions for x and y into the original function to get the image function

#y=-2x^3+6x#

#rArr(y'-4)/2=-2((x'+1)/4)^3+6((x'+1)/4)#

Simplify to your heart's content!