Until this point, all graphs have come from an equation that contains an x and a y variable. These variables indicate the input and output values and correspond to the x and y-axes. Now, functions will be modeled using a new notation.

For functions, "y =" and "f(x) =" (pronounced "f-of-x") mean the exact same thing. However, "f( x)" allows for more flexibility and more information. Instead of saying "y = 2x + 3; solve for y when x = -1", the new notation says "f(x) = 2x + 3; find f(-1)". In either case, the same thing needs to be done: substitute -1 for x, multiply by 2, and then add 3, simplifying to get an output value of 1. Using the first notation, the final statement becomes; when x = -1 then y = 1. In the second notation, this would be written f(-1) = 1.

Function notation allows greater flexibility than using just "y" for every formula. Graphing calculators will list different functions as y1, y2, etc. Textbooks use names like f(x), g(x), h(t), s(t), etc. With this notation, more than one function at a time can be used without confusing or mixing up the formulas.


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