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 (1,1) , 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) . 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 (1,3) , and the translated function is y=f(x−2)

Answer 1

To determine the effect of the horizontal translation on the point (1, 1) and the function \( y = f(x) \), we need to know the direction and magnitude of the translation.

1. If the function is translated to the right by 2 units, the point (1, 1) will move to (3, 1). The translated function would be written as \( y = f(x - 2) \).

2. If the function is translated to the left by 2 units, the point (1, 1) would stay at (1, 1), and the translated function would be \( y = f(x + 2) \).

Based on the information provided in the potential responses and the nature of the translation, the correct response is:

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