Test 1 Prep

composition of functions/function comp

(fog)(x)=f(g(x))

decreasing function

a function "f" is said to be decreasing on an interval "i" if f(x1) >f(x2) whenever x<x2

increasing function

a function "f" is said to be increasing on an interval "i" if f(x1) < f(x2) whenever x<x2

complex number

a number written in the from a+bi where "a" and "b" are real numbers. where the real part is a and b and the imaginary part is i.

function

a relation where each element in the domain corresponds to exactly one element in the range

one to one function

each element (x-value) in the domain corresponds to only one element in the range (y value) and each element (y value) in the range corresponds to exactly one element (x value) back in the domain.

inverse function

if "f" is a one to one (1-1) function with domain x and range y then there exists an inverse function denoted f^-1(x), with domain y and range x.

remainder therorem

if P(x) is a polynomial, c is a real or nonreal complex number, and P(x) is divided by x-c, then the remainder is P(c)

vertical line test

if any vertical line can be drawn so that it only intersects a graph at only one poiny, then the graph is a function

rational functions

let P(x) and Q(x) be polynomials where Q(x) does not equal 0. then P(x)/Q(x) is a rational expression. (the ratio of polynomials)

factor theorem

let P(x) be a polynomial and let "c" be a real or non-real number. if P(c)=0, the x-c is a factor of f(x), and if x-c is a factor of P(x), the P(c)=0.

horizontal line test

let f be the graph of a function. if any horizontal line can be drawn so that it only intersects the graph of f at only one point, the f is a 1-1 function

vertical asymptotes

the line x=a is a vertical asymptote for the graph as a function "f" if f(x)-> -infinity as x->a

horizontal asymptotes

the line x=b is a horizontal asymptote for the graph when f(x)->b as x=> infinity or as x->- infinity