Question

If f(5)= 3, write an ordered pair that must be on the graph of y = f(x + 1) + 2

Answer 1

f(5) = 3 means (5,3) is on the graph of f.

On the new graph, y = f(x+1) + 2, what do the +1 and +2 do?

Things inside the function notation inpact the x-values, since that's where x sits.

This outside the f(x) notation impact the y-values, since those are done after you've evaluated the function.

"+1" on the inside shifts every point to the left 1 unit.  (Inside changes are almost always opposite from what it looks like it would do.)

"+2" on the outside will shift every point up by 2 units.

So what do you get if you take (5,3) and shift it left 1 and up 2?