The RHIC-STAR (Relativistic Heavy Ion Collider-Solenoid Tracker at RHIC) experiments have measured the cumulants of net-proton (a proxy for net-baryon), net-charge, and net-kaon (proxy of net-strangeness) multiplicity distributions in Au+Au collisions at different centers of mass with energies ranging from 7.7 GeV to 200 GeV. Recent results have shown that the ratio of the fourth-order net-proton cumulant over the second-order one ($\kappa {\sigma }^{\mathrm{2}}$) exhibits a nonmonotonic energy dependence. In relativistic heavy-ion collision experiments, only information about the final state particles can be measured. Therefore, we investigated the fluctuations of the conserved charges (baryon, electric charge, and strangeness) in Au+Au collisions using a multiphase transport (AMPT) model. This model can basically describe the results measured by the RHIC-STAR experiment. More importantly, the AMPT model is used to understand the key impacts of the dynamical evolution of relativistic heavy-ion collisions on fluctuations and correlation functions, including the creation and diffusion of conserved charges, hadronization, hadronic rescatterings, and weak decays. It was discovered that the correlation between positive and negative charges may originate from the string melting mechanism. Baryon (proton) correlation functions are consistent with the expectation of baryon number conservation. Net-strangeness (net-kaon) originates from pair production. We studied the correspondence between representative quantities and their conserved charges and found that their behaviors are qualitatively consistent yet quantitatively different. Although the physics of quantum chromodynamics (QCD) critical fluctuations is not included in the AMPT model, our results are expected to provide a baseline for the search of possible critical behavior at the QCD critical end point in relativistic heavy-ion collisions. We incorporated critical density fluctuations into the model and found that they play a role.