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

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
g left parenthesis y right parenthesis equals y

g(y)=y+1

Answer 1

To identify the correct function that shows the translation from the point \((2, -5)\) to the point \((2, -6)\), we need to understand that the translation affects the \(y\)-coordinate while the \(x\)-coordinate remains the same.

The change is as follows:
- Starting point: \((2, -5)\)
- Ending point: \((2, -6)\)

The \(x\)-coordinate stays at \(2\), while the \(y\)-coordinate changes from \(-5\) to \(-6\). This means that we are translating downwards by 1 unit, which can be represented in a function for \(y\).

In this case, we can describe this translation using a function for the \(y\)-coordinate:

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

This function reduces the \(y\)-value by 1, correctly representing the translation from \(-5\) to \(-6\).

Thus, the appropriate function that shows the translation is:

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