Math 103: College Algebra and TrigonometryExam 2 study outlineSection 3.1: Functions• Identify functions• Find the domain and range of functionsSection 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 lineSection 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 functionsSection 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 transforma-tions applied to itSection 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 andwhether 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 vertexof 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 functionSection 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 = xnlooks like, for various nonnegative integer valuesof 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 touchesthe x-axis there• Know how the degree of a polynomial function relates to the maximum number ofturning points (local maxima and local minima) it can have• Understand end behavior of polynomialsPage 1Section 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 asymptotesSection 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 graphSection 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 setSection 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 polynomialwith integer coefficients• Use these tools to find the real zeros of a polynomial function• Intermediate Value TheoremSection 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 = HPage