# Functions Examples

In math, a function is an equation or expression that includes one or more variables, or unknown numbers, and the "output" of the function (the answer to the express) will depend on the "input," or the number used in place of the variable.

Functions are often notated with an f(x). This means the "function of x," where x is the variable. A simple function might be notated this way:

f(x)=3x

So, the function is to multiply by 3. So, for every value that is put in for x, the output, or answer, would be different:

f(2) |
6 |

f(3) |
9 |

f(4) |
12 |

f(6) |
18 |

f(7) |
21 |

f(10) |
30 |

f(20) |
60 |

Notice that the function of x, or the variable, depends on what the mathematical expression says to do. The function is a *relationship* between the "input," or the number put in for x, and the "output," or the answer. So the relationship between 20 and 60, for example can be described as "3 times 30 is 60."

While the most common notation for functions is f(x), the actual notation can vary. It can be anything: g(x), g(a), h(i), t(z). The letter or symbol in the parentheses is the variable in the equation that is replaced by the "input."

More Function Examples

f(x) = 2x+5

The function of x is 2 times x + 5.

f(10) |
25 |

f(100) |
205 |

f(50) |
105 |

f(2) |
9 |

f(5) |
15 |

g(a) = 2+a+10

The function of a is 2+a+10.

g(4) |
16 |

g(6) |
18 |

g(10) |
22 |

g(24) |
36 |

g(30) |
42 |

f(n) = 6n+4n

The function of n is 6 times n plus 4 times n.

f(3) |
30 |

f(15) |
150 |

f(50) |
500 |

f(100) |
1,000 |

f(2) |
20 |

x(t) = t÷2

The function of t is t divided by 2.

x(48) |
24 |

x(500) |
250 |

x(24) |
12 |

x(60) |
30 |

x(100) |
50 |

f(e) = 100e-50

The function of e is 100 times e minus 50

f(10) |
950 |

f(100) |
9,950 |

f(2) |
150 |

f(3) |
250 |

f(5) |
450 |

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