Yes, you can provide liquidity over the full price range like in Uniswap v2, but your rate of return will be significantly lower than a similar position with a more narrow price range.
To add liquidity in the Full Range, press the ‘Full Range’ button. This will set your min price to 0 and your max price to infinity.
Please read on to learn more about the relative inefficiency of a Full Range position compared to a concentrated liquidity position over a more narrow range.
Full Range in Uniswap v2
In Uniswap v2, all LPs provided liquidity across the "full range" of the price curve from zero to infinity. Much of that liquidity was never utilized because assets tend to trade within a price range more narrow than zero to infinity. This was a relatively capital inefficient strategy for liquidity providers because the market price is unlikely to reach those extreme prices for many assets.
Concentrated Liquidity in Uniswap v3
Uniswap v3 solves this problem by introducing concentrated liquidity. In v3, LP’s can provide liquidity within a custom price range in order to efficiently allocate capital in a selected range. This allows LPs to provide greater amounts of liquidity at desired prices, and no liquidity at extreme prices which they do not expect to occur in the market.
What happens if you take a Full Range position in Uniswap v3?
Your LP position will earn fees, but at a lower rate than even modestly more narrow price ranges. If you never want to worry about your position going out of range, this could be a viable choice for you. Alternatively, you could consider a slightly more narrow range (e.g. 1 to 1M - depending on the asset pair) in order to earn a higher rate of return while maintaining a low risk of going out of range.
You can compare your expected fees per dollar of liquidity using the simulator tool in this blog post.