# Continuity of Functions Terms

## Get down with the lingo

### 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 there are constants,

*M*and

*N,*with

*M*<

*f*(

*x*) <

*N*for all values of

*x*in the domain.

### Unbounded Function

A function*f*(

*x*) is unbounded if there are no constants,

*M*and

*N*, with

*M*<

*f*(

*x*) <

*N*for all values of

*x*.The function extends to infinity or negative infinity somewhere in its domain.