# Functions, Graphs, and Limits

### Terms

### Limit

The value that the value of a function*f*(

*x*) approaches as the input

*x*approaches a specific value.

### Piecewise Function

A function defined on an interval expressed as multiple sub-functions, each defined on sub-intervals.### 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.

### Horizontal Asymptote

A horizontal line that a function*f(x)*approaches as

*x*approaches +infinity or -infinity.

### Vertical Asymptote

A vertical line*x*=

*a*if

*f(x)*approaches

*+infinity or -infinity as*

*x*approaches

*a*from right or left.

### Slant Asymptote

A line*y*=

*mx*+

*b*of a function

*f*(

*x*) if

*f*(

*x*) approaches

*mx*+

*b*as

*x*approaches infinity.

### Curvilinear Asymptote

A line if*f*(

*x*) approaches a curve as

*x*approaches infinity.

### Hole Of A Function

A value of*x*where the function has no value.

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