Question

what determines the traits of offspring

Answer 1

Genes come in different varieties, called alleles. Somatic cells contain two alleles for every gene, with one allele provided by each parent of an organism. It is impossible to tell exactly what gene the organism could have. 

Answer 2

traits are determined by the traits the current parent(s) have, it can enhariate both dominant and recessive genes.

if an offspring carries a recessive trait over a dominate, the offspring will carry It as a dominant trait to its offspring.