A linear parent function is the equation y = x or f(x) = x. A parent function is the simplest equation of a function. Thus, f(x) = x is the simplest of all linear functions and that is the reason why it is called linear parent function.

You can make a table of values to graph this function. See the table below.

x | y = x |

0 | 0 |

1 | 1 |

2 | 2 |

3 | 3 |

-1 | -1 |

-2 | -2 |

-3 | -3 |

Here is the graph for this function.

We only show 7 points. However, the graph has infinitely many points.

Therefore, the domain is the set of real numbers and the range is the set of real numbers.