Although it is normal to regard the quantity demanded and the quantity supplied as functions of the price of the goods, the standard graphical representation, usually attributed to Alfred Marshall, has price on the vertical axis and quantity on the horizontal axis.
Since determinants of supply and demand other than the price of the goods in question are not explicitly represented in the supply-demand diagram, changes in the values of these variables are represented by moving the supply and demand curves (often described as "shifts" in the curves). By contrast, responses to changes in the price of the good are represented as movements along unchanged supply and demand curves.
A supply schedule is a table that shows the relationship between the price of a good and the quantity supplied. Under the assumption of perfect competition, supply is determined by marginal cost. That is, firms will produce additional output while the cost of producing an extra unit of output is less than the price they would receive.
A hike in the cost of raw goods would decrease supply, shifting costs up, while a discount would increase supply, shifting costs down and hurting producers as producer surplus decreases.
By its very nature, conceptualizing a supply curve requires the firm to be a perfect competitor (i.e. to have no influence over the market price). This is true because each point on the supply curve is the answer to the question "If this firm is faced with this potential price, how much output will it be able to and willing to sell?" If a firm has market power, its decision of how much output to provide to the market influences the market price, therefore the firm is not "faced with" any price, and the question becomes less relevant.