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

Answer 1

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: \( f(x) = x + 2 \).