Plotting graphs in C[a,b]

Folks,

If given p =3 and q=6 any numbers and the set $\displaystyle \{f \in \mathbb[C} [a,b]: p\ge f(x) \le q \forall x \in [a,b]\} $

Is my graph of f(x)=x^3 +3 shown in this wolfram link correct based on this set?

plot y(x)=x^3+3 between 3 and 6 - Wolfram|Alpha

1) What norm is this C[a,b] is representing...is it a sup norm, taxi cab norm?

2) What is the effect if the C[a,b] with sup norm is required?

Thanks

Re: Plotting graphs in C[a,b]

The sup norm **is** the standard norm on C[a,b] (the set of functions continuous on the interval [a, b]).

Re: Plotting graphs in C[a,b]

Quote:

Originally Posted by

**HallsofIvy** The sup norm **is** the standard norm on C[a,b] (the set of functions continuous on the interval [a, b]).

Ok, another question suppose I have $\displaystyle \{f,g \in \mathbb{C} [a,b]: p\ge || f(x)-g(x)|| \le q \forall x \in [a,b]\} $

How would I plot this assuming we know the functions ie, f(x)=x^3+3 and g(x)=x-1. Will the sup norm norm involve max{|f(x)|,|g(x)| for plotting?

Thanks

Also posted here but will keep each forum informed of responses. Thanks

Functions in Normed Linear Space