Question

On this coordinate plane, point A (-2, 3) is translated into point A′ (3, 5) . Which functions give the two translations?

f(x) = x + 2 and g(y) = y + 5

f(x) = x + 5 and g(y) = y + 2

f(x) = x - 5 and g(y) = y - 2

f(x) = x + 6 and g(y) = y + 3

Answer 1

To find the functions that describe the translations of point A (-2, 3) to point A′ (3, 5), we need to determine how the x-coordinate and y-coordinate change.

1. **For the x-coordinate**:
- The original x-coordinate is -2 and it translates to 3.
- The change in the x-coordinate is 3 - (-2) = 3 + 2 = 5.
- This means we are adding 5 to the x-coordinate:
\[
f(x) = x + 5.
\]

2. **For the y-coordinate**:
- The original y-coordinate is 3 and it translates to 5.
- The change in the y-coordinate is 5 - 3 = 2.
- This means we are adding 2 to the y-coordinate:
\[
g(y) = y + 2.
\]

Now, we can summarize the translations as follows:
- For the x-coordinate: \( f(x) = x + 5 \)
- For the y-coordinate: \( g(y) = y + 2 \)

Thus, the correct functions that describe the translations are:
**f(x) = x + 5 and g(y) = y + 2**.