Use the image to answer the question.

Question

Two curves drawn on coordinate plane. Both axes range from negative 5 to 5 in unit increment.

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 (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)
.
The point is located at left parenthesis 1 comma 1 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)
.

Answer 1

To determine the location of the point and the translated function, we need to identify the nature of the horizontal translation of the function \(y = f(x)\).

1. The original function goes through the point (1, 1).
2. If the function undergoes a horizontal translation, to the right by 2 units, the new point will shift from (1, 1) to (3, 1).
3. The translated function will then take the form \(y = f(x - 2)\) to reflect this shift.

Thus, the correct answer is:

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

This translates to the two statements:

• 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.