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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 (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)
.
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 .
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1 answer

To determine the new position of the point (1, 1) after a horizontal translation and identify the translated function, we need to know the direction and magnitude of the horizontal translation.

  1. If it is a translation to the right, we would use \( f(x - h) \), where \( h \) is the distance of the translation. If it is a translation to the left, we use \( f(x + h) \).

Assuming the translation given in the options suggests a shift to the right by 2 units (check the responses), then:

  • The original point (1, 1) would become (3, 1) after a translation to the right by 2 units.
  • The translated function, based on the rightward translation of 2 units, would be \( y = f(x - 2) \).

Following this understanding, the correct response would be:

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