Question

Use the image to answer the 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 (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 (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)

Answer 1

To determine the correct translation and the new location of the point (1,1) after a horizontal translation, we need to understand how translations affect the coordinates of points in a function.

1. **Horizontal Translation**: If the function \( y = f(x) \) undergoes a horizontal translation to the right by \( c \) units, the new function will be \( y = f(x - c) \) and any point \( (x_0, y_0) \) on the original function will move to the point \( (x_0 + c, y_0) \). Conversely, if it moves to the left, the new function will be \( y = f(x + c) \).

2. **Applying Logic**: From the options given, we need to check for a right translation and ensure any point maintains its y-coordinate while changing its x-coordinate accordingly.

The point (1,1) translated to the right by 2 units will move to:
- \( (1+2, 1) = (3, 1) \)
And the translated function would be:
- \( y = f(x - 2) \)

Based on this understanding:

The correct answer appears to be:
- The point is located at \( (3, 1) \), and the translated function is \( y = f(x - 2) \).