**Preface**

This series is aimed at providing tools for an electrical engineer to analyze data and solve problems in design. The focus is on applying calculus to equations or physical systems.

**Introduction**

This article will introduce functions.

There are many calculus references, the one I like to use is Calculus by Larson, Edwards and Hostetler.

This also assumes you are familiar with Python or can stumble your way through it.

**Concepts***Variable: *a symbol used to hold a value or coordinate.*Coordinate: *a set of numbers used to indicate the position of a point, line, or plane. In the form of *(a,b,c,...,n)* and usually (x,y) and (x,y,z).*Function: *a real-valued function f of a real variable *x* from *X* to *Y* is a correspondence that assigns to each number *x* in *X* exactly one number *y* in *Y*; where *X* and *Y* are sets (of anything) and *x* and *y* are variables.*Intercept: *a coordinate at which one coordinate value in the set is zero.*Intersection: *a coordinate at which two sets of data (or functions) intercept.*Graph: *a visual representation of coordinate sets, most often in 2 to 4 variables.*Slope: *rate of change of a function

m=(y_{2}-y_{1})/(x_{2}-x_{1}), x_{1} != x_{2}

**Linear Functions**

General Form | Ax+By+C=0 |

Vertical Line | x=a |

Horizontal Line | y=b |

Point-slope Form | y-y_{1}=m(x-x_{1}) |

Slope-intercept Form | y=mx+b |

Where A, B, C, y_{1}, x_{1}a and b are coordinates; m is a the slope; x and y are variables.

**Function Transformations**

Original Graph (Reference) | y=f(x) |

Horizontal Shift | y=f(x±c) |

Vertical Shift | y=f(x)±c |

Reflection (about x) | y=-f(x) |

Reflection (about y) | y=f(-x) |

Reflection (about origin) | y=-f(-x) |

**Next Up**

Continuity and Limits of functions.

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