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Infinitely many. There is a different shaped graph for each function that can exist. Plus there are graphs for non-functional measures. One of my favourites is Minard's graph depicting the losses sustained by Napoleon's army in Russia. See link.
People use line graphs in businesses, and to compare data. Line graphs are mostly used when people are entrepreneurs. They figure out profit this way. Line graphs are also used when a product is made. They decide if they should continue to make this product, by how well the product sells. Line graphs show the change.
Either a straight line through the origin or a hyperbola.
Exponential growth goes infinitely up. Exponential decay goes infinitely over always getting closer to the x axis but never reaching it. ADDED: An exponential decay trace's flat-looking region has its own special name: an "asymptote".
Intercept for a graph are points at which the graph crosses either axis. There is no such thing as an intercept for tables.