Question

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?

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