# Algebra II Terms

## Get down with the lingo

### Base

The number an exponent is "attached" to (what a leech) in its superscript. In a logarithm, it's located in the subscript (the number below the log).### Common Logarithm

A logarithm with a base of 10. It's usually written all sneakily without a base as log*x*, but sometimes it shows up as log

_{10 }

*x*.

### Exponential Decay

The ever-decreasing quality of an exponential function with a base*b*that's in between 0 and 1.

### Exponential Function

A function with the*x*in the exponent over a constant base, which grows or decays depending on the value of the base. Coefficient optional, like mayonnaise.

### Exponential Growth

The ever-increasing quality of an exponential function with a base*b*> 1.

### Inverse Function

Given a function*f*(

*x*), the inverse function

*f*

^{ -1}(

*x*) is a new function where the input and output values are swapped. Translation: (

*a*,

*b*) becomes (

*b*,

*a*) for every single point on the graph.

### Inverse Operation

A symbol that reverses the original operation, given the same input. Think about adding 2, then subtracting 2.### Logarithmic Function

A function containing a logarithm, which rises quickly at very low values of*x*and then puts on the brakes

*hard*to slow down at higher values of

*x*.

### Logarithmic Scale

A graphing scale that increases at an exponential rate. It's usually recognizable by tick-marks at powers of 10 and weird googly eyes attached.### Natural Logarithm

A logarithm with a base of*e*, often written as

*ln*. Contains no preservatives.