The fish in the picture is a female molly, and it is a dalmation (black & white spotty pattern) and it has the lyretail.
Female mollies, platies, swordtails & guppies have a fan or triangle shaped anal (bottom) fin.
Male mollies, platies, swordtails & guppies have a long thing anal fin called a gonopodium.
-------------------
Common livebearers like guppies, platies and swordtails need a pH above 7.0 and a GH (general hardness) around 200ppm.
Mollies need a pH above 7.0 and a GH above 250ppm.
If the water is too soft (lacking minerals), they have problems.
If the pH is below 7.0, they can have problems.
If the fish look off colour or one dies, do a 75% water change and gravel clean the substrate every day for a week. And post some pictures here along with information about the tank.
Make sure any new water is free of chlorine/ chloramine before it's added to the tank.
The following link has information about what to do if your fish get sick. It's long and boring but worth a read when you have some spare time.
If your fish ever looks sick or unwell, then the following steps might help. Test the Water and Clean the Tank. Test the water quality for ammonia, nitrite, nitrate and pH and write the results down in numbers. Check it for general hardness (GH) and carbonate hardness (KH) too if you can, but...
www.fishforums.net
-------------------
What sort of filter is in/ on the tank?
Did the shop tell you how to clean the filter?
Did the shop tell you about the filter cycle?
Did the shop tell you about water changes and feeding?