Essential Functions – A Gateway to Calculus

Essential functions are a part of pre-calculus that is learned before getting into real calculus (derivatives, integrals, differential equations. These functions have to be familiar because they will occur often in the field. We are going to examine some essential functions and give an overview of how they are used in calculus

Linear functions: these are you basic straight line functions with the form y=mx+b. Where m is the slope of the graph and b is the y-intercept.

Polynomial functions; These equations will look like this; y=x^2+3x+1. where the degree of the polynomial gets higher as the power of x gets higher. Polynomials of degree 2 are quadratics, 3 are cubic, and 4 are quartic.

Power functions; these equations are written as x^a, where ‘a’ is some constant number. When a is 1 we have a straight line, when it is 2 a parabola.

Rational functions; Functions that are the division of two polynomials in the form f(x)=p(x)/q(x)

Exponential functions; These equations have the form of a^x, where a can be any constant. The most common value for a is Euler’s number, e, which is approximately 2.71828

Logarithmic functions; these are the inverse of exponential functions. These function have a base as well. Logarithms with base e take on the symbol of ‘ln(x)’.

So there is a review of essential functions for calculus. You will surely see them again when you start learning about derivatives, so it is important to know all these by memory.