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2024-08-21

Full / hollow dot at the end of graphs

$\sqrt{x^{2}} = | x |$

One to one: (of a function) has an inverse. Can be tested with the horizontal line test

\begin{aligned} f \circ f^{- 1} (x) & = x for dom f^{- 1} \\ f^{- 1} \circ f (x) & = x for dom f \end{aligned}

Don't confuse $\sin^{- 1} x$ with $(\sin x)^{- 1}$
Prefer $\arcsin$ and $a s i n$ to $\sin^{- 1}$

Factorization of cubes:

\begin{aligned} a^{3} - b^{3} & = (a - b) (a^{2} + a b + b^{2}) \\ a^{3} + b^{3} & = (a + b) (a^{2} - a b + b^{2}) \end{aligned}

Point-slope form: $y - y_{o} = m (x - x_{o})$

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