Pre-calculus is function literacy. Calculus asks how functions change, so this course makes sure you can describe a function's domain, shape, asymptotes and inverse before differentiating it.
Practise derivativesA function assigns exactly one output to each input. Domain and range questions are therefore about legality, no division by zero, no even roots of negatives, no logs of non-positives.
Transformations act predictably: changes outside the function move the graph vertically and behave as written, while changes inside move it horizontally and behave in reverse.
Sketching a polynomial needs only roots with multiplicities and end behaviour. Odd multiplicity crosses the axis, even multiplicity touches and turns back.
For rational functions, vertical asymptotes come from surviving denominator zeros, holes from cancelled factors, and horizontal behaviour from comparing degrees of numerator and denominator.
Exponential and logarithmic functions are inverses, so their graphs reflect across the line y = x and their domains and ranges swap. This symmetry explains every log domain restriction.
Arithmetic sequences add a constant difference; geometric sequences multiply by a constant ratio. Infinite geometric series converge exactly when the ratio has magnitude below one.
Vectors carry magnitude and direction. Adding components independently and using the dot product for angles covers most of the pre-calculus treatment.
A limit describes the value a function approaches, not the value it takes. Substitute first; if that gives an indeterminate form, factor, rationalise or simplify until it no longer does.
