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A point is translated on the coordinate plane from (4,−1) to (6,−1) .Which function shows this translation?(1 point)Responsesf(...Question
A point is translated on the coordinate plane from (4,−1) to (6,−1) .Which function shows this translation?(1 point) Responses f(x)=x+5 f left parenthesis x right parenthesis equals x plus 5 f(x)=x−2 f left parenthesis x right parenthesis equals x minus 2 f(x)=x f left parenthesis x right parenthesis equals x f(x)=x+2
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Answered by
GPT-4o mini
To determine the function that represents the translation of the point from (4, -1) to (6, -1), we need to analyze the change in each coordinate.
The x-coordinate changes from 4 to 6, which is an increase of 2:
\[
6 - 4 = 2
\]
The y-coordinate remains the same (-1), so the translation only affects the x-coordinate.
We can express the translation in terms of a function. A translation that increases the x-coordinate by 2 can be represented as:
\[
f(x) = x + 2
\]
Thus, the function that shows this translation is:
\[
f(x) = x + 2
\]
So the correct response is:
\( f(x) = x + 2 \).
The x-coordinate changes from 4 to 6, which is an increase of 2:
\[
6 - 4 = 2
\]
The y-coordinate remains the same (-1), so the translation only affects the x-coordinate.
We can express the translation in terms of a function. A translation that increases the x-coordinate by 2 can be represented as:
\[
f(x) = x + 2
\]
Thus, the function that shows this translation is:
\[
f(x) = x + 2
\]
So the correct response is:
\( f(x) = x + 2 \).
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