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3.4 Vocabulary for Graphs and Domains of Logarithmic Functions   

Critical Numbers

Inputs that make a function output 0 or undefined.    Used as endpoints on a sign chart.  

Domain of a function

The set of input values which yield an output value.  The set of “allowable values” for the input.

e

An irrational number, often defined as

                                        .

 and is used to model situations involving  continuous growth or decay.

Exponential function

A function whose output changes by a percentage amount for each unit change in the input.  The rate of change, therefore is NOT constant like it is with a linear function.  Exponential functions can either exhibit growth or decay.

Logarithm

The power you raise 10 to in order to get the desired number.  For example

Natural Exponential Function

An exponential function having the number e as the base.

Sign chart

An organizational tool used to keep track of the sign (positive or negative) of the function outputs in certain intervals.  Normally, the endpoints of the intervals are the critical numbers  of the function.

Vertical Asymptote

A vertical asymptote occurs at a finite value,  , when the output values grow larger and larger, either positively or negatively, as x approaches a .

Symbolically we write:

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