A demand curve is Price vs. Quantity, holding all else constant; whereas, a demand function is Quantity vs. Price, holding all else constant. If you can imagine a graph, with the y-axis being Price, and the x-axis being Quantity, and you were to plot price/quantity data or, perhaps, even a function onto this graph, then that would be a demand curve. If you did something similar but, this time, the y-axis was Quantity, and the x-axis was Price, then what you would have, instead, is what is called a demand function.
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