Question: 

What are  Autorange - AutoVolt - Vchek - LoZ

Answer: 

       AC/ DC   and    Voltage/Current   are separate functions on Fluke meters, ie    AC V  or   DC V  or  AC A   or  DC A. 
“Auto range” refers to the size of the measurement in that function eg    1.000  or  10.00  or  100.0    For example if the 10.00 V range is manually selected and greater than 10.0 V is applied the meter would show “O/L” . If auto range is selected the meter would automatically re-range to the range best suited to the measurement.  Auto range will not change the function.

All Fluke handheld meters have the option for auto range on the selected function but only the 287 and 289 have the option to display the separate components of a combined AC + DC voltage.  See pages 26/27 of the user guide (pages 36/37 of 88 in this pdf)…
https://dam-assets.fluke.com/s3fs-public/287_289_umeng0200.pdf




Auto Volt & LoZ modes are options on the   289, 114, 116, 117     “Vchek” is a permanent mode on the 113.

Auto Volt
Automatically selects the AC or DC function determined by the larger part of an applied voltage.  This requires DC coupling into a true RMS measurement circuit that will show the voltage level of both AC and DC or a combined signal. 
https://en.wikipedia.org/wiki/True_RMS_converter
On the 289 it behaves in a similar way to the AC + DC function, see page 23 of the user guide (page 33 of 88 in the pdf – link above)
On the 11x series it displays only AC or DC,  See table 1 on page 2 of the user guide (page 6 of 22 in this pdf)…
https://dam-assets.fluke.com/s3fs-public/110__117umeng0000_0.pdf

Vchek
Uses Auto Volt technology but if no voltage is detected the 113 switches to resistance (continuity) mode.

LoZ  
The significant difference in this voltage mode is that the input impedance of the meter drops from 10MΩ to 3kΩ, this has the side effect of drawing more current and will trip a 30mA RCD if placed across Live to Earth at 230V.
The main purpose of the LoZ  mode is to dispel “Ghost” or Induced Voltages, these are caused by parasitic capacitive coupling.
please see these web links for more information…
https://en.wikipedia.org/wiki/Capacitive_coupling#Parasitic_capacitive_coupling

Dual impedance detail:
https://www.fluke.com/en-gb/learn/blog/digital-multimeters/dual-impedance-digital-multimeters
https://dam-assets.fluke.com/s3fs-public/2718074_6116_ENG_A_W.PDF
https://dam-assets.fluke.com/s3fs-public/6002580_6003_ENG_B_W.PDF
https://dam-assets.fluke.com/s3fs-public/2747091_6003_ENG_A_W.PDF
https://www.youtube.com/watch?v=mRwsxmn2P-s