How would you do this: Find f(x+Δx) for f(x) = x2 – 2x – 3 without knowing anything about derivatives

This is a question on my summer math packet for Calculus AB AP. I haven't learned anything about derivatives yet but when I tried to google this question to find a way to approach it almost all the hits involved derivatives, which I do not know how to do yet.

f(x) = x² – 2x – 3
Now write (x + Δx) in place of x
f(x + Δx) = (x + Δx)² – 2(x + Δx) – 3

It is straightforward, you just have to replace x by x+h in the expression of you function (h means delta x here, which is nothing but a notation)...

f(x+h)= (x+h)^2 - 2(x+h) - 3 = (x^2 +h^2 + 2hx) - 2x-2h -3 = x^2 +x(2h-2) + h^2 -2h -3

With this expression you see that f(x+h) = f(x) + h^2 - 2h + 2xh

And then if you need (f(x+h)-f(x))/h you will find h-2+2x

Now if you take h as small as possible (in absolute value), which means h tends to zero then you will find the derivative function of your function : namely g(x)= 2x-2

Indeed the definition of the derivative function (if it exists in a given interval) of a function f, is the limit when h tends to zero of the following expression: (f(x+h)-f(x))/h

If it said "write an expression for f(x + y) if f(x) = x^2 - 2x -3", would you know what to do? Do that!

Now imagine that "delta x" is just another way of writing "y". You can now write out an expression for "f(x + delta x)"