Determine the discontinuity at the given point and identify it as infinite, jump, or removable.

Infinite discontinuity – When a function increases or decreases indefinitely at a given point.

Example:

x | -0.01 | -0.001 | 0 | 0.001 | 0.01 |
---|---|---|---|---|---|

f(x) | – |

Infinite

Jump discontinuity – At a given point the function on the left and the right have two distinct values.

Example:

x | -2.1 | -2.01 | -2 | -1.99 | -1.9 |
---|---|---|---|---|---|

f(x) | -7.1 | -7.01 | – | 2.96 | 2.61 |

Jump

Removable discontinuity – The function is continuous except for a hole at the given point.

Example:

x | -3.01 | -3.001 | -3 | -2.999 | -2.99 |
---|---|---|---|---|---|

f(x) | -0.166 | -0.167 | – | -0.167 | -0.167 |

Removable,

x | 2.99 | 2.999 | 3 | 3.001 | 3.01 |
---|---|---|---|---|---|

f(x) | -100 | -1000 | – | 1000 | 100 |

Infinite