I am a visual artist. I built a studio on my house. can i deduct the addition

Assuming the house is your primary residence, you really have nothing to "deduct" per-se. What you have is a home office, and you can claim a home office which will result in deductible depreciation that you can take each year, or you can elect the "standard deduction" for the home office. Test both to see which is better for you. You'll deal with this in the Business Income & Expenses (SCH C) section of the program where it asks if you have a home office. Just answer that question yes and work it through. Here's some additional info you will need in order to correctly complete the Home Office (HO) section.
What you spent for the add-on adds to your cost basis for the house. So if you originally purchased the house years ago for $250,000, and spent $102,000 for the additional room, your total cost basis is now $352.000 on the house. Now if you enter data in the program correctly, here's how this will work for you.

You will be taking depreciation on the house each year. THe amount of depreciation you are allowed to take each year depends on:
 - THe percentage of the total square footage of the house that is designated as a Home Office for "business use only" and;
 - The percentage of time business is conducted in that space, and;
 - The percentage of business that is conducted in that space.

I need to define some things for you, so you will be clear on what the program is asking you for as you work this through.

Percentage of time you conduct business in the home office - This *must* be 100% (one hundred percent). Anything less, and you do not qualify for the home office deduction. Basically what you are saying is that any time I am in that space, I am conducting business. Now understand you may only use that space for business for say, 1 hour a day 3 days a week. But for that time, if you are in that space, you are conducting business and *nothing* else. The kids don't use that room for playing their video games, and the wife doesn't use it as a sewing room.

Percentage of business conducted in the home office - This very well can (and most likely will) be less than 100%. Maybe you spend 20% of your business time visiting client locations and taking pictures. Then the other 80% of your time is spent in the home office editing those pictures.

Now, you will also be able to claim a portion of your household utility expenses too, among other things. So it's important to pay attention to each screen and read it completely before making selections or entering data. The program will ask you for two types of expenses.

You will be asked for "whole house" expenses. For example, you will be asked what you spent for utilities for the "whole house" for the year (or from the time you placed the HO "in service"). Then you will be asked what you spent for utilities for the "home office only". So unless you have a separate electric meter and water meter for the home office, your "home office only" expenses will most likely all be zero.

You will have more questions as you work this through. But so as not to inundate you with "information overload" I'll stop here so you can get started on this. Just ask questions as they arise and you'll be fine.