Question

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
(3,1) is where point is
Translation function
y = f(x + 2)
y = f(x - 2)

Answer 1

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 \( y = f(x - 2) \).