MATH12550_Fall2019_Lecture07_worksheet_Exam1_studyguide.pdf

MATH 12550.00 - Lecture 7 - Exam 1 study guide (1.1-1.7, 2.1-2.3, 3.1-3.6) 1. Functions Evaluating a function at numbers and/or variables (#1-2) Vertical line test for functions (#3-6) Computing average rate of a function and difference quotient (#7-11) Algebra of functio...

MATH 12550.00 - Lecture 7 - Exam 1 study guide (1.1-1.7, 2.1-2.3, 3.1-3.6) 1. Functions Evaluating a function at numbers and/or variables (#1-2) Vertical line test for functions (#3-6) Computing average rate of a function and difference quotient (#7-11) Algebra of functions: add, subtract, multiply, divide Composition of functions (#18-20) Finding inverse of functions (#30-31) Identifying features of functions from a graph: intercepts, increasing, decreasing, local min/max (#16-17) Domain/range of a function from graph/expression (#12-13) Graphing basic functions/piecewise functions (#14-15) Transformations of functions (#21-24) Even/odd functions (#25-26) Absolute value functions, equations, inequalities (#27-29) 2. Linear Functions Writing down equation of a line: slope-intercept, point-slope (#32-33) Parallel/perpendicular lines (#37-41) Graphing lines (#34-36) Identifying whether a function is linear from graph/table/data (#42-43) Modeling with a linear function (#44-46) 3. Quadratic functions Complex numbers and their operations (#47-49) Solve quadratic equations (#50-51) Graph quadratic functions, identify vertex, intercepts (#52-55) Solving application problems, finding vertex (#56) Correspondence between the graph of a quadratic function, the discriminant, and the type of roots (#57-58) 4. Polynomial Functions Identify degree, leading coefficient and end behavior (#59-63) Local behavior of polynomials: number of roots, number of turning points, type of roots and their local graphs (#64-65, #76-79) Writing down an expression from a graph of a polynomial (#66-67) 1 CC BY: Tatyana Khodorovskiy  Graphing a polynomial from expression or known roots (#68-69,80) Long division of polynomials (#71-72) Finding roots of polynomials, using the remainder/factor/rational root theorem (#73-75) Using Intermediate Value Theorem (#70) 2 CC BY: Tatyana Khodorovskiy