5 MathJax Test

1.1  Length of a Vector

It follows from the Pythagorean formula that the length $\|\mathrm{a}\|$ of $\mathbf{a}=\left\langle a_{1}, a_{2}\right\rangle$ satisfies $\|a\|^{2}=a_{1}^{2}+a_{2}^{2} .$

This is shown in the following image:

Thus we get

$\|a\|=\sqrt{a_{1}^{2}+a_{2}^{2}} \text {. }$

Example: Use the graph of $y=g(x)$ to sketch the graphs of:

$y=g\left(x+2\right)-1$