Math 103 College Algebra and Trigonometry Exam 2 study outline Section 3 1 Functions Identify functions Find the domain and range of functions Section 3 2 The Graph of a Funciton Identify the graph of a function vertical line test Get information about a function from its graph domain range intercepts values Section 3 3 Properties of Functions Identify even and odd functions both graphically and algebraically Determine where a function is increasing decreasing or constant Find local minima and local maxima Average rate of change equation of secant line Section 3 4 Library of Functions Piecewise defined Functions Know what the graphs of common functions look like y x y x y 3 x y x2 y x3 y x y 1 x Find values domain range of piecewise defined functions Graph piecewise defined functions Section 3 5 Graphing Techniques Transformations Change a function in order to transform the graph in a certain way shift left shift right shift up shift down stretch or compress horizontally stretch or compress vertically reflect about the x or y axis Given a function interpret it as a common function from Section 3 4 with transformations applied to it Section 4 3 Quadratic Functions and Their Properties Identify quadratic functions Graph a quadratic function using transformations or otherwise Know how to find the vertex axis of symmetry and intercepts of a parabola and whether it opens up or down use these facts to graph a parabola Find the maximum or minimum value of a quadratic functions by finding the vertex of its graph Section 4 4 Quadratic Models Building Quadratic Functions from Data Interpret a word problem and model it with a quadratic function Maximize or minimize such a quadratic function Section 5 1 Polynomial Functions and Models Identify polynomial functions Understand that polynomial functions are always smooth and continuous Know how to find the degree leading term and leading coefficient of a polynomial Understand what the graph of y xn looks like for various nonnegative integer values of n Identify the real zeros x intercepts of a polynomial function and their multiplicity Know how the multiplicity of a zero determines whether the graph crosses or touches the x axis there Know how the degree of a polynomial function relates to the maximum number of turning points local maxima and local minima it can have Understand end behavior of polynomials Page 1 Section 5 2 Properties of Rational Functions Identify rational functions Find the domain of a rational function Put a rational function in lowest terms Find vertical asymptotes horizontal asymptotes and oblique asymptotes Section 5 3 The Graph of a Rational Function Find the domain Find the y intercept if 0 is in the domain Write the function in lowest terms Find x intercepts zeros of the numerator when written in lowest terms Determine behavior near each x intercept Find vertical asymptotes zeros of the denominator when written in lowest terms Find horizontal or oblique asymptotes Divide x axis into intervals and plot one point in each interval Analyze behavior near each asymptote Complete the graph Section 5 4 Polynomial and Rational Inequalities Move everything to the left hand side Determine where the function is positive negative or zero to find the solution set Section 5 5 The Real Zeros of a Polynomial Function Know the Remainder Theorem and the Factor Theorem and how to use them Find the maximum number of real zeros a polynomial function can have Use the Rational Zeros Theorem to identify all possible rational zeros of a polynomial with integer coefficients Use these tools to find the real zeros of a polynomial function Intermediate Value Theorem Section 6 1 Composite Functions Understand what composite functions are Given two functions f and g find the composite functions f g g f and f f evaluate f g x for a given value of x Find the domain of a composite function Given a function H find two functions f and g such that f g H Page 2