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?

a. f (x) = x - 1
b. g (y) = y - 1
c. g (y) = y
d. g (y) = y + 1

Answer 1

To translate the point (2, -5) to (2, -6), we are changing the y-coordinate from -5 to -6 while keeping the x-coordinate the same.

This means we need to apply a transformation to the y-coordinate only. The translation can be represented as:

\[
y' = y - 1
\]

In this case, if we let \(y\) be the original y-coordinate (-5), then the new y-coordinate \(y'\) after the translation becomes:

\[
y' = -5 - 1 = -6
\]

So, the appropriate function that represents this translation is:

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

Thus, the correct option is:

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