Tax rates are marginal. So for instance if the tax rate was 20% up to $100k, then 30% afterward, you'd pay 20% on your first $100k, then 30% from $100,001 and up.
That introduces some distortions into house pricing, making it very difficult to sell a house in the £250,000 to £265,000 range - because you are competing with houses just under the threshold which work out significantly cheaper for the buyer. As someone selling a house which falls into that price range, you might be better off asking for slightly less from the sale (versus asking for just over the threshold and waiting much longer to find a buyer).
But the step function thing was the point, not the taxes. I'll put in an edit and get that last bit ignored.
(1) Be careful what you take as truth when young and don't rethink later.