Let $S$ be a set of objects, and suppose $w$ is a weight function on $S$ with generating function $\Phi_S(x)$. Let $w^*$ be a new weight function for $S$ defined by $w^*(a)=5w(a)+3$ for all $a\in S$, and let $\Phi^*_S(x)$ be the generating function for $S$ with respect to $w^*$. Express $\Phi^*_S(x)$ in terms of $\Phi_S(x)$.
How would I do this problem? Is there some general method for linearly changing the weight function? Google seems to be extremely unhelpful with my introductory combinatorics course.