Given that (5,-8) is on the graph of f(x) , find the corresponding point for the function f(x+2)

(3,-8)

Explanation:

Here you must consider the rules of translation of functions.

Specifically the rule to apply here is for the addition of a constant to the argument of a function, i.e. x.

The argument of the function f(x) is x. The argument of the functio f(x+2) is x + 2. The rule is: when you add a constant value, name it k, to the argument of a function, the graph is shifted  k units to the left.

So, here you are adding 2 to the argument, meaning the point (5, -8) will end two units to the left ⇒ (5 - 2, 8) = (3,8). And that is the answer.