# Continuity of Functions

### Terms

### Continuity

A function*f*(

*x*) is continuous at the point

*x*=

*a*if some small change in

*x*results in small changes in the values of

*f*(

*x*).

### Maximum Value

The largest value(s) that a function assumes on an interval.### Minimum Value

The smallest value(s) that a function assumes on an interval.### Left-hand Limit

The value a function*f*(

*x*) approaches as the input

*x*approaches a specific value from the left.

### Right-hand Limit

The value a function*f*(

*x*) approaches as the input

*x*approaches a specific value from the right.

### Bounded Function

A function*f*(

*x*) is bounded if

*f*(

*x*) is less than or equal to a constant |

*f*(

*x*)| <=

*M*for all values of

*x*in the domain.

### Unbounded Function

A function*f*(

*x*) is unbounded if a constant

*M*such that |

*f*(

*x*)| <=

*M*does not exist for all values of

*x*.

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