Question

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? (1 point)
○ g(y)=y - 2
○ f(x)=x + 2
● g(y)=y + 2
○ g(y)=y

Explanation:

Step1: Analyze x - and y - coordinate changes

The x - coordinate remains the same (4) for both points (4, - 8) and (4, - 6). The y - coordinate changes from - 8 to - 6.

Step2: Find the change in y - coordinate

The change in the y - coordinate is $\Delta y=-6-(-8)=-6 + 8=2$. This means the point is translated 2 units up in the y - direction.

Step3: Determine the function

A function that represents a vertical translation of a point's y - coordinate by 2 units up is $g(y)=y + 2$.

Answer:

C. $g(y)=y + 2$