Math Exponential functions Natural exponential function

# Natural exponential function

The natural exponential function is often referred to as e-function. The name comes from the Euler number $e$, which forms the basis of the exponential function for an e-function. The e-function has the function equation:

$y=e^x$
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### Remember

The Euler number is denoted by $e$ and, like $\pi$ is a constant, irrational number. The Euler number has the value $e = 2,7182818...$.
i

### Tip

The derivative of the e-function $f(x)=e^x$ is also $f'(x)=e^x$. The following applies:
$f(x)=f'(x)$

This is the e-function with $f(x)=e^x$:

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### Properties

• The range of values $W=[0,\infty]$ and the domain $D=\mathbb{R}$ (real numbers)
• The e-function has no zeros, because the x-axis is an asymptote (graph approaches, but never reaches)
• The intersection with the y-axis is at $P(0|1)$.
• The graph monotonically increases