# Plotting graphs in C[a,b]

• Dec 7th 2011, 12:19 PM
bugatti79
Plotting graphs in C[a,b]
Folks,

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

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

plot y&#40;x&#41;&#61;x&#94;3&#43;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
• Dec 7th 2011, 02:09 PM
HallsofIvy
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]).
• Dec 7th 2011, 02:33 PM
bugatti79
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 $\{f,g \in \mathbb{C} [a,b]: p\ge || f(x)-g(x)|| \le q \forall x \in [a,b]\}$

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