a) Let c R, > 0, and set (K) = u + c for u

a) Let c ∈ R, δ > 0, and set τ(K) = δu + c for u ∈ R. Prove that if (ɸ, I) is a smooth parametrization of some curve, if J = τ-1(I), and if ψ = ɸ o r, then (ψ, j) is orientation equivalent to (ɸ, I).
b) Prove that if (ɸ, I) is a parametrization of some smooth arc, then it has an orientation equivalent parametrization of the form (ψ[0, I).
c) Obtain an analogue of b) for piecewise smooth curves.