Question

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?(1 point)
Responses

g(y)=y
g left parenthesis y right parenthesis equals y

f(x)=x−1
f left parenthesis x right parenthesis equals x minus 1

g(y)=y−1
g left parenthesis y right parenthesis equals y minus 1

g(y)=y+1

Answer 1

To find the function that shows the translation of the point from (2, -5) to (2, -6), we need to focus on the change in the y-coordinate, since the x-coordinate remains the same.

The original point has a y-coordinate of -5, and the translated point has a y-coordinate of -6. The change in the y-coordinate can be expressed as:

\[
-5 \rightarrow -6
\]
This means we are moving down by 1 unit. Therefore, to express this transformation as a function, we can define a function \( g(y) \) that subtracts 1 from the y-coordinate:

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

To verify, if we input -5 into this function:
\[
g(-5) = -5 - 1 = -6
\]
This confirms the function correctly translates the point from (2, -5) to (2, -6).

Therefore, the appropriate translation function is:

**g(y) = y - 1.**