##<b>Types of functions.</b> Let $a, a_0, a_1, \ldots, a_n, b, m$ be real numbers. #A linear function is of the form $mx+b$ ($m$ is the slope, $b$ is the $y$-intercept) #A polynomial function is of the form $a_n x^n+a_{n-1}x^{n-1}+\cdots+a_2x^2+a_1x+a_0$ #A power function is of the form $x^a$ ($a$ is the fixed exponent or power) #A root function is of the form $x^{1/n}=^n\sqrt{x}$ #A rational function is of the form $\frac{p(x)}{q(x)}$, where $p$ and $q$ are polynomials #An algebraic function is a function that can be constructed from polynomials using algebraic operations ($+$, $-$, $\cdot$, $/$, $x^a$) repeatedly. #A basic trigonometric function is one of $\sin x$, $\cos x$, $\tan x$, $\mbox{csc} x$, $\mbox{sec} x$, $\mbox{cot} x$ #An exponential function is of the form $a^x$, where $a>0$ (can you see why the base $a$ should be positive?) #A logarithic function is of the form $\log_a x$, where $a>0$ is the fixed base