Section+2.2--Polynomial+functions+of+Higher+Degree

Section 2.2--//Polynomial functions of Higher Degree// Polynomial Function Let n be a nonnegative integer and let an, an-1,..., a2, a1, a0 be real numbers with an cannot equal 0. The function f(x) = anx^n + an-1x^n-1 + ... + a2x^2 + a1x + a0 is called a polynomial function of x with degree n. The coefficient an is called the leading coefficient.

f(x) = c Constant Function Horizontal Line f(x) = mx + b Linear Function Line --> Slope =m Y intercept = (0, b) f(x) = ax^2 +bx +c Quadratic Function Parabola --> Opens up if a > 0. Opens down if a < 0.

Power Function Let n be a positive integer and the coefficient a cannot equal 0 be a real number. The function f(x) = ax^n is called a power function of degree n.

Immediate Value Theorem Let a and b be real numbers such that a < b and let f be a polynomial function. If f(a) and f(b) have opposite signs, then there is at least one zero between a and b.