unit ball of dual space in R

Question

I want to sketch the unit ball in the dual of $R$, the unique linear formes defined on $R$ have the forme $f(x)=ax$ with $a$ is reel, so $${B^*} = \{ f(x) = ax/\sup |ax| < 1{\text{ for |x| = 1\} }}$$ i fond that the elements of this ball are the function of the forme $ax$ with $|a|<1$ ? Is that true ? thanks.