A family Φ of continuous real-valued functions on a space X is said to be basic if every f∈C(X) can be represented f=∑i=1ngi∘ϕi for some ϕi∈Φ and gi∈C(R) (i=1,…,n). Define basic(X)=min{|Φ|:Φis a basic family forX}. If X is separable metrizable then either X is locally compact and finite-dimensional, and basic(X)<ℵ0, or basic(X)=c.If K is compact and finite-dimensional then basic(K)⩽cof([w(K)]ℵ0,⊆), and if K contains a discrete subset D with |D|=w(K), then either K is finite-dimensional, and basic(K)=cof([w(K)]ℵ0,⊆) or basic(K)=|C(K)|=w(K)ℵ0.