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.
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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 \( y = f(x + c) \).
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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 \( y = f(x - 2) \).