Question

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

Answer 1

`(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!