[MATH 123] - Final Exam Guide - Everything you need to know! (24 pages long)
Document Summary
Rule that assigns each input value x in some set a unique output value f(x). Y is dependent variable, x is independent variable. Ex: surface area is a function of volume of a balloon. Ways to represent functions: verbally, numerically (table of values), visually (graph), algebraically (formula). Domain of a function: the set of all input values x for which the function f(x) is defined. Finding domain: any thing that makes denominator zero, the inside of an even root negative, and restrictions from the question (explicitly stated or through nature of question) Range of a function: set of output values for function f(x) Finding domain: sketch graph or think through constraints on range. Graph of a function is {(x, f(x))| x is in the domain of f(x). That is, the set of all points in the cartesian plane defined by the equation y=f(x) Ways to draw graphs: table of values, apply transformations to basic graphs, use calculus.
