Function Notation: Introduction

Function Notation

Introduction

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.