graphing functions

Question

Given the coordinates (2,-8) are on the graph of y = f(x) what would the coordinates be after the following transformation?

y = f(-x+5) + 7

Answer 1

Let me rephrase the question.

We are told that f(2) = -8.

We are given g(x) = f(-x+5)+7.

The question is "For what value x can be determine g(x)".

The answer is that x must be such that

-x+5 = 2

That is

x = 3

And

g(3) = f(2)+7 = -8+7 = -1.

The coordinates sought in the original question are (3, -1).