Algebraic functions are functions which can be expressed using arithmetic operations and whose values are either rational or a root of a rational number. Now, we will be dealing with transcendental functions. Transcendental functions return values which may not be expressible as rational numbers or roots of rational numbers. Algebraic equations can be solved most of the time by hand.
Terminology[ edit ] There are many terms for tetration, each of which has some logic behind it, but some have not become commonly used for one reason or another. Here is a comparison of each term with its rationale and counter-rationale.
The term tetration, introduced by Goodstein in his paper Transfinite Ordinals in Recursive Number Theory  generalizing the recursive base-representation used in Goodstein's theorem to use higher operationshas gained dominance. It was also popularized in Rudy Rucker 's Infinity and the Mind.
The term superexponentiation was published by Bromer in his paper Superexponentiation in The term hyperpower  is a natural combination of hyper and power, which aptly describes tetration. The problem lies in the meaning of hyper with respect to the hyperoperation sequence.
When considering hyperoperations, the term hyper refers to all ranks, and the term super refers to rank 4, or tetration.
So under these considerations hyperpower is misleading, since it is only referring to tetration. The term power tower  is occasionally used, in the form "the power tower of order n" for.Definition of Exponential Function The function f defined by.
where b > 0, b 1, and the exponent x is any real number, is called an exponential function. In the case of exponential functions it is sometimes convenient to write the exponential function in “point-base” form.
Point base form is: y = y 1a x• 1; and is called “point-base” form because you can see the base a and the point (x 1;y 1) in the equation. In this section we will introduce exponential functions. We will be taking a look at some of the basic properties and graphs of exponential functions. We will also discuss what many people consider to be the exponential function, f(x) = e^x.
Precalculus Here is a list of all of the skills students learn in Precalculus!
These skills are organized into categories, and you can move your mouse over any skill name to preview the skill. Graphing exponential functions is similar to the graphing you have done before. However, by the nature of exponential functions, their points tend either to be very close to one fixed value or else to be too large to be conveniently graphed.
Jul 24, · How to Write an Exponential Function Given a Rate and an Initial Value. In this Article: Article Summary Using the Rate as the Base Using "e" as the base Community Q&A.
Exponential functions can model the rate of change of many situations, including population growth, radioactive decay, bacterial growth, compound interest, and much more%(1).