All great questions. Let's tackle them one by one:
> is it possible for the supply and demand functions not to intersect?
For this to happen, the quantity that consumers would be willing to purchase at every given price would have to be lower than the quantity producers are able to supply at every given price. But if this were the case, then no trades would be occurring, and we couldn't really call that a market.
> Also, are these functions usually straight lines, or in the real world, are the usually curved?
When I am not doing quick and dirty models to demonstrate the upward/downward pressure of prices created by changes in supply/demand, drawing them as curves is actually more appropriate. The law of decreasing marginal returns should lead to demand curves being curved, and the law of increasing marginal costs should lead to supply curves being curved.
> is it possible for the supply and demand functions not to intersect?
For this to happen, the quantity that consumers would be willing to purchase at every given price would have to be lower than the quantity producers are able to supply at every given price. But if this were the case, then no trades would be occurring, and we couldn't really call that a market.
> Also, are these functions usually straight lines, or in the real world, are the usually curved?
When I am not doing quick and dirty models to demonstrate the upward/downward pressure of prices created by changes in supply/demand, drawing them as curves is actually more appropriate. The law of decreasing marginal returns should lead to demand curves being curved, and the law of increasing marginal costs should lead to supply curves being curved.