Giving that (4,-8) is on a graph of f(x) find the corresponding point for the function f(x+3)

(1,-8)

Going from f(x) to f(x+3) has you shift the entire graph of f(x) 3 units to the left. In other words, you subtract 3 from each x coordinate. So that's why we go from (4,-8) to (1,-8) since 4-3 = 1 is the result of subtracting 3 from the x coordinate. The y coordinate stays the same the whole time.