A demand curve is always downward sloping.Discuss.More is always demanded at a lower price than at a higher price.

Although this is generally a true statement, it is not
alway true.

In general, people do demand more of a product
when it is at a low price and less of it when it is at a high
price.

However, it is at least theoretically possible to
have a product for which demand is perfectly inelastic.  For such a product, people will
buy the same amount regardless of the price.  Here, the demand curve is
vertical.

It is also possible for a product to have
perfectly elastic demand where people will buy a given product, but only at one price. 
Here, the demand curve is horizontal.