Given that (7, -6) is on the graph of f(x) , find the corresponding point for the function f(x+2)

The point (7,-6) means x = 7 and y = -6 pair up. Recall that y = f(x). So if y = -6, then f(x) = -6 as well when x = 7. So f(7) = -6

Compare f(7) with f(x+2). We see that x+2 = 7 must be true. Isolate x by subtracting 2 from both sides

x+2 = 7

x+2-2 = 7-2

x = 5

The new x coordinate is x = 5. The y coordinate stays the same.

If we were to plug x = 5 into f(x+2), we would get

f(x+2) = f(5+2) = f(7) = -6

The input x = 5 leads to the output f(x+2) = -6

Visually, the point (7,-6) has been shifted 2 units to the left to land on (5,-6)

i believe the answer is c.