For the kinds of functions you will meet in statistical computing there are only three mathematical rules that you need to learn: these are concerned with powers, exponents and logarithms. In the expression xb the explanatory variable is raised to the power b. In ex the explanatory variable appears as a power – in this special case, of e = 2.71828, of which x is the exponent. The inverse of ex is the logarithm of x, denoted by log(x) – note that all our logs are to the base e and that, for us, writing log(x) is the same as ln(x).
It is also useful to remember a handful of mathematical facts that are useful for working out behaviour at the limits. We would like to know what happens to y when x gets very large (e.g. x → ∞) and what happens to y when x goes to 0 (i.e. what the intercept is, if there is one). These are the most important rules: