What you’ll learn
Represent transformations as functions.
Key idea
For a preimage undo each shift, then undo the first-coordinate sign; each input has one image.
A preimage undoes shifts and sign; changing the written vertical operation is not the function.
Worked example
Enter the exact value or ordered values in the format requested below.
T(x,y)=(-1x+(2),y+(2)). Find the unique image of input (-2,-2).
- First image coordinate -1(-2)+(2)=4.
- Second image coordinate -2+(2)=0; image (4,0). The inverse is x=-1(x_image-(2)), y=y_image-(2).
Answer: (4,0)
Quick Check
Evaluate a worked attempt at represent transformations as functions, identify the first invalid step, and provide the correction.
T(x,y)=(-1x+(1),y+(-2)); input (-2,-1). Student: Step 1, x_image=3. Step 2, y_image=-1-(-2)=1. Identify the first invalid step and correct the image.