1. ## Confused about: g(x) and h(x)

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.

2. ## Re: Confused about: g(x) and h(x)

Originally Posted by Googl
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.
I am not sure what the phrase "I don't understand the use of g(x)" means. I understand the following phrases: "I don't understand why ... (e.g., this is true")," "I don't understand what ... (e.g., this sentence is saying)," "I don't understand how ... (e.g., the author derived this equality)." So, please explain more precisely what you don't understand. In this problem, f(x) and g(x) are two unrelated functions.

Originally Posted by Googl
Somewhere in the example workout it says:

g(x) = (x - 1)^2
so -> g(x) = f(x - 2)
This must be a different g(x).