The the original function goes through (1,1) and is translated using a horizontal translation where is the point located after the translation and what is the translation function

To find the translation function that moves the point (1, 1) to (3, 1), we need to look at the changes in the x-coordinates since the y-coordinate remains the same.

1. The original point is (1, 1).
2. After the translation, the new point is (3, 1).

We see that the x-coordinate changes from 1 to 3, which is a horizontal translation to the right by 2 units.

The translation function can be written as:

\[
y = f(x - 2)
\]

This indicates that to obtain the original function \( f \), you need to replace \( x \) with \( x - 2 \).

Summary:
- After the translation, the point is located at (3, 1).
- The translation function is \( y = f(x - 2) \).