Polynomial Functions

Polynomials are the gentlest functions we meet in calculus — smooth, predictable, and built from nothing more than powers of $x$ with constant coefficients. A polynomial function like $f(x) = 3x^2 - 5x + 2$ is defined for every real $x$, and its graph is a continuous, unbroken curve with no sharp corners or gaps. Because they are so well-behaved, polynomials form the perfect starting point for learning how to differentiate and integrate — every rule you di …