A point is translated on the coordinate plane from (4, -8) to (4, -6). Create a function to show this translation. Which function shows the appropriate translation?

Question

a. g (y) = y
b. g (y) = y - 2
c. g (y) = y + 2
d. f (x) = x + 2

Answer 1

To find the appropriate function that describes the translation of the point from \( (4, -8) \) to \( (4, -6) \), we focus on the change in the y-coordinate.

The y-coordinate changes from \(-8\) to \(-6\), which is an increase of \(2\). We can represent this translation using a function that takes the y-coordinate as input and outputs the new y-coordinate after the translation.

The function that reflects this translation can be expressed as:

\[ g(y) = y + 2 \]

This function adds \(2\) to the original y-coordinate. So when you input \(-8\) into the function:

\[ g(-8) = -8 + 2 = -6 \]

This matches the new y-coordinate after the translation.

Therefore, the correct option is:

c. \( g(y) = y + 2 \)