The original function y=f(x) in the graph (solid line) goes through the point (1,1) and is translated using a horizontal translation. Where is this point located after the translation, and what is the translated function?

Question

(1 point)
Responses

The point is located at (3,1), and the translated function is y=f(x−2).
The point is located at left parenthesis 3 comma 1 right parenthesis , and the translated function is f left parenthesis x minus 2 right parenthesis .

The point is located at (1,3), and the translated function is y=f(x−2).
The point is located at left parenthesis 1 comma 3 right parenthesis , and the translated function is f left parenthesis x minus 2 right parenthesis .

The point is located at (3,1), and the translated function is y=f(x+2).
The point is located at left parenthesis 3 comma 1 right parenthesis , and the translated function is f left parenthesis x plus 2 right parenthesis .

The point is located at (1,1), and the translated function is y=f(x−2).

Answer 1

To determine the location of the point (1,1) after a horizontal translation and the translated function, we need to know the specifics of the translation.

1. For a horizontal translation to the right by 2 units, the function \(y = f(x)\) becomes \(y = f(x - 2)\). Thus, the point (1,1) will move to (3,1).

2. For a horizontal translation to the left by 2 units, the function \(y = f(x)\) becomes \(y = f(x + 2)\). In this case, the point (1,1) would move to (-1,1).

Since we are looking for a translation specified as \(x - 2\) or \(x + 2\), the correct answer would be:

The point is located at (3,1), and the translated function is \(y = f(x - 2)\).