What is the Natural Base Exponential Function?

Note:

The natural base exponential function is actually a function that's shorter than its name! This tutorial introduces you to this special function and shows you what it looks like.

Keywords:

definition
natural base
exponential function
e

Background Tutorials

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
- What is the X-Axis?
  
  To graph a function or plot an ordered pair, you need to use a coordinate plane, so you should learn all about it! In this tutorial, you'll learn about the x-axis and see where it's located in the coordinate plane.
Know and apply the properties of integer exponents to generate equivalent numerical expressions.
- What are Exponents?
  
  Did you know that another word for 'exponent' is 'power'? To learn the meaning of these words and to see some special cases involving exponents, check out this tutorial!
Use the properties of exponents to transform expressions for exponential functions.
- What's an Exponential Function?
  
  Looking at an equation with a variable in the exponent? You have an exponential function! Learn about exponential functions in this tutorial.
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
- What is Domain?
  
  Did you know that a relation has a domain? The domain of a relation is the set of the first coordinates from the ordered pairs. This tutorial defines the domain of a relation!
- What is the Range of a Relation?
  
  Did you know that a relation has a range? The range of a relation is the set of the second coordinates from the ordered pairs. This tutorial defines the range of a relation!
Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
- What is e?
  
  In math, 'e' isn't just a letter, it's an irrational number! This tutorial shows you how mathematicians use the letter 'e' to represent a specific value and how having a base of 'e' is called a natural base.