Functions which intersect asymptote $y=ax+b$ infinitely many times

Question

I'm looking for a case similar to $f(x)=\frac{sin(x)}{x},\ y=0$. But I need a function $f(x)$ with the asymptote $ax+b,\ a\ne 0$.

Answer 1

sin(x)+x with asymptote y=x-something, adjust it with coefficients like a sin(x) + bx