A point is translated on the coordinate plane from (2,−5) to (2,−6) . Create a function to show this translation. Which function shows the appropriate translation?

Question

A. g(y) = y
B. f(x) = x - 1
C. g(y) = y + 1
D. g(y) = y - 1

Answer 1

To translate the point \((2, -5)\) to \((2, -6)\), we notice that the x-coordinate remains the same (2), while the y-coordinate changes from \(-5\) to \(-6\).

This represents a downward shift of 1 unit in the y-direction. Therefore, we need a function that takes \(y\) and subtracts 1 to achieve the change in the y-coordinate.

The function that accomplishes this is:

\[ g(y) = y - 1 \]

This function takes any y-value and reduces it by 1, which corresponds to the downward translation observed.

So, the correct answer is:

D. g(y) = y - 1.