Height functions on singular surfaces parameterized by smooth maps $$\mathcal {A}$$-equivalent to $$S_k$$, $$B_k$$, $$C_k$$ and $$F_4$$

We describe singularities of height functions on singular surfaces in $$\mathbb {R}^3$$ parameterized by smooth map-germs $$\mathcal {A}$$ -equivalent to one of $$S_k$$ , $$B_k$$ , $$C_k$$ and $$F_4$$ singularities in terms of extended geometric language via finite succession of blowing-ups. We investigate singularities of dual surfaces of such singular surfaces.