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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 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 (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 .
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1 answer

To determine the new location of the point (1, 1) after a horizontal translation, we need to know the direction and amount of the translation.

Since it sounds like we are given a horizontal translation that moves the graph to the right, we would typically express this as \( f(x - h) \), where \(h\) is the amount of translation. If we assume the translation is 2 units to the right, the new function would be \(f(x - 2)\).

Thus, the original point (1, 1) would move to:

  • New x-coordinate: \(1 + 2 = 3\)
  • y-coordinate: Stays the same, so it remains 1.

So after the translation, the point (1, 1) shifts to (3, 1).

Putting this all together, the correct response would be: The point is located at (3, 1), and the translated function is \(y = f(x - 2)\).