Direction of a European put when rates rise

Holding everything else fixed, suppose the risk-free interest rate goes up. What happens to the value of a European put? Reply $1$ if it rises, $0$ if it is unaffected, or $-1$ if it falls.

$-1$ (the put loses value). The put's holder receives the strike $K$ at expiry, and a higher rate shrinks its present value $Ke^{-rT}$. Equivalently, higher rates raise the forward price, which helps calls and hurts puts, so put rho is negative.