I am revising on sketching curves. But I am very confused about the following even though I have become very good at sketching graphs.

An example from the book is:

Given that:

i) f(x) = x^3

ii) g(x) = x(x - 2)

Sketch the curves with equation y=f(x + 1) and g(x +1)

I don't understand the example that the book provides. Not because I don't know how to sketch the curve but the use of g(x) is what I don't understand. Somewhere in the example workout it says:

g(x) = (x - 1)^2

so -> g(x) = f(x - 2)

Also

h(x) = x^2 + 2

so -> h(x) = f(x) + 2

Please help as I would like to finish this chapter sooner. The use of h(x) and g(x) is what I don't understand. I will also appreciate any links that you may provide.

Thanks.