1. Review Math 140Exam 2

2. Chapter 3 Recognize a graph as belonging to one of the function families whose portraits appear in the introduction. Determine precisely how modifications to a function will affect its graph. Recognize even or odd functions by graph or formula Find the algebraic formula for the composition of two functions. Work backward from a composite function to find simpler functions that produced it. Determine the domain of a composite function. Determine from a graph whether it is one-to-one and thus has an inverse. Given the graph of a one-to-one function, sketch the graph of the inverse function. Given algebraic formulas for two functions, test whether or not they are inverses. Find the algebraic formula for the inverse of a function. Know the relationship between domain/range of a function and domain/range of its inverse. Progress Check

3. Apply the laws of exponents to algebraic expressions (4.1) Write exponential models (4.1) Approximate an instantaneous rate of change, the slope of a curve at a point (4.2) Convert exponential functions from standard form to base-e form and vice-versa (4.2) Use a logarithm scale to rescale data that vary widely in magnitude (4.3) Translate exponential statements into logarithmic statements (4.3) Sketch graphs of logarithmic functions (4.3) Use the definition and the properties of logarithms to simplify expressions containing logarithms (4.3, 4.4) Use logarithms in solving equations (4.3, 4.4) Given a logistic model, find and interpret its point of inflection and its carrying capacity (4.5) Progress Check Chapter 4

4. Sketch a graph of any quadratic function. This includes locating any intercepts and finding the coordinates of the vertex (5.1) Approximate the instantaneous rate of change of a function at a point (5.1) Interpret the coordinates of the vertex of a parabola in the context of an optimization problem (5.1) Find the zeros of a polynomial function (5.2) Determine the global behavior of a polynomial function (5.2) Find the vertical asymptotes of a rational function (5.3) Find the horizontal asymptotes of a rational function (5.3) Recognize polynomial functions and rational functions from their graphs (5.2, 5.3) Sketch a rough graph of a polynomial or rational function using a grapher to refine your picture (5.2, 5.3) Interpret characteristics of polynomial or rational functions in context (5.1,5.2, 5.3) Chapter 5 Progress Check