Fourier Transform of exponential
The plot is of $$\mid X\left(i\omega\right) \mid = \sqrt{\left(\frac{1}{a+j\omega}\right)\left(\frac{1}{a-j\omega}\right)} = \frac{1}{\sqrt{a^2 + \omega^2}}$$ 

against $\omega$

In particular $\omega$ can be equal to $-a$. 

This checks out with Wolfram alpha