Understanding the Domain and Range of eᵡ
The domain of eᵡ is all real numbers, allowing you to plug any real number into x. eᵡ will produce a real number as output. In mathematical terms, the domain is represented as Domain = ℝ.
The range of eᵡ is all real numbers greater than 0. This means that eᵡ will always output a positive real number. In mathematical terms, the range is represented as Range = (0, ∞).
Table of Values for eᵡ
This table below shows how different x-values produce corresponding eᵡ values. These pairs of numbers can be points on the graph of eᵡ.
| x | eᵡ |
|---|---|
| -5 | 0.0067 |
| -2 | 0.1353 |
| -1 | 0.3679 |
| 0 | 1 |
| 1 | 2.7183 |
| 2 | 7.3891 |
| 5 | 148.4132 |
As you can see, as x increases, eᵡ also increases rapidly. Conversely, as x decreases, eᵡ approaches zero but never actually reaches it.
