A point is translated on the coordinate plane from \((4,-1)\) to \((6,-1)\). Which function shows this translation?

Question

A. \(f(x)=x+5\)
B. \(f(x)=x+2\)
C. \(f(x)=x-2\)
D. \(f(x)=x\)

Answer 1

To understand the translation from the point \((4, -1)\) to \((6, -1)\), let's analyze the change in the x-coordinate.

The original point has an x-coordinate of 4, and after translation, the x-coordinate becomes 6. The change in the x-coordinate can be calculated as follows:

\[ 6 - 4 = 2 \]

Since the y-coordinate remains the same throughout this translation (\(-1\) remains \(-1\)), the translation modifies only the x-coordinate by adding 2.

This means that the function representing this translation can be written as:

\[ f(x) = x + 2 \]

Given the options, the correct answer is: B. \(f(x) = x + 2\).