I know that Live View can be used, at least on some cameras, to keep the mirror up and avoid mirror slap (as described at Can anything be done to reduce the shutter sound on my SLR?), but when I turn on Live View on my D3300 and take a picture, the monitor goes black and I hear the slap anyway. Then, Live View returns on the monitor. How can I avoid this?
Most DSLR cameras with Live View have several options for how autofocus is achieved when shooting in LV. Some of those options will use the Phase Detection AF system that is normally used when shooting with the viewfinder. There are usually other options that allow for Contrast Detection AF using the camera's imaging sensor. This allows the camera to take a photo without cycling the mirror.
The D3300 as well as other Nikon entry level DSLRs has another consideration. The mechanism that provides the mechanical movement needed to stop down the lens' aperture immediately before the shot is taken is the same mechanism that moves the mirror. In order to leave the lens' aperture all the way open when composing the shot, the mirror must be cycled to provide the mechanical movement needed to close the aperture down to the selected setting via the mechanical linkage from the camera body to the lens.