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?


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
g left parenthesis y right parenthesis equals y plus 1

g(y)=y

Answer 1

To determine the correct translation function for moving a point from (2, -5) to (2, -6) on the coordinate plane, we first note that the x-coordinate remains the same (2) while the y-coordinate changes from -5 to -6.

This means we are moving the point down by 1 unit in the y-direction.

To express this as a function:
- The original y-coordinate is -5.
- The new y-coordinate after translation is -6, which can be expressed as \(y - 1\).

This means that our translation function for the y-coordinate will subtract 1:

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

In conclusion, the correct function that shows the translation is:

\(\mathbf{g(y) = y - 1}\)