I am going to sell my rental home to my child and will be gifting part of the value of the house. Home value is 450,000. Gift is 100,000. My basis is 350,000.

What is your question?
Is your Basis $350,000 AFTER adjusting for depreciation?

My basis would be $340,000

Any answers on this?

As I asked before, what is your question?

The question is what will I owe in capital gains?  I'm wondering if the gift will offset any capital gain?

For tax purposes, the sales price is what you actually receive.

So if you receive $350,000 and your Adjusted Basis is $340,000, then $10,000 will be subject to taxes.

The depreciation is taxed at your regular tax rate, up to 25%, a Gain of $10,000 would likely result in $2500 in Federal taxes (but it could affect other things on your tax return as well).

However, your child's Basis will also be $350,000.  So if your child were to immediately sell it for $450,000, your child would have a $100,000 taxable gain.