Expert: Paul Klarreich - 6/8/2006

Question
summarize the general function of exponential and logarithmic functions, give an example of each, and explain the characteristics of the graphical representation of each.

Answer
Hi, Jannie,

Subject:  help summarize
Question:  summarize the general function of exponential and logarithmic functions, give an example of each, and explain the characteristics of the graphical representation of each.
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You are asking for a lot here, and I will just get you started; the rest you can get from any calculus (or even precalculus) text.

An exponential function is one containing a power in which the exponent contains a variable.  The simplest is called THE exponential function,  y = e^x, sometimes written  y = exp(x).

Since e^x can never be negative, the graph is always positive, and it is asymptotic to the negative side of the x-axis.

A logarithmic function contains a logarithm of an expression containing a variable.  The simples is called the NATURAL logarithm function, written y = ln(x), and it is the inverse of the exponential.  Since it is the inverse, its graph is the same as the graph of  y = exp(x) when reflected across the line  y = x.

That ought to be enough for now.