# Functions, Graphs, and Limits Terms

## Get down with the lingo

### 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 ± ∞.

### Vertical Asymptote

A vertical line,*x*=

*a*, where

*f*(

*x*) approaches ± ∞ as

*x*approaches

*a*from the right or left.

### Slant Asymptote

A line,*y*=

*mx*+

*b*, that a function approaches as

*x*approaches infinity.

### Curvilinear Asymptote

A non-linear function that another function,*f*(

*x*), approaches as

*x*approaches infinity.

### Hole Of A Function

A value of*x*(call it

*a*) where

*f*(

*a*) doesn't exist but the limit as

*x*approaches

*a*does.

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