\documentstyle[12pt]{report} \setlength{\oddsidemargin}{0.0in} \setlength{\textwidth}{6.5in} \setlength{\topmargin}{0.0in} \setlength{\headheight}{0.0in} \setlength{\headsep}{0.0in} \setlength{\textheight}{9in} \begin{document} \noindent {\large\bf Information for Test 2} \bigskip \noindent {\bf Office Hrs:} Extra (R: 1:30-2:30), Usual (R: 4-6). \noindent {\bf Calculator:} OK. (But the use of a graphing calculator may be restricted on some problems.) \bigskip \noindent {\bf Advice:} Look over old quizzes and HW problems. If you missed points on a problem, know why you missed them! \bigskip \noindent {\bf Test Covers:} \begin{itemize} \item 2.6--2.7 \vspace{-2mm} \item 3.1--3.5 \vspace{-2mm} \item 4.1--4.6 \end{itemize} \bigskip \noindent {\bf Details:} \begin{itemize} \item Chapter 2: Composition of functions. 1-1 functions and their inverses. \vspace{-2mm} \item Chapter 3: Graphing polynomial functions. Real roots. Complex numbers and their properties. Fundamental Theorem of Algebra. Graphing rational functions. \vspace{-2mm} \item Chapter 4: Exponential and logarithmic functions. Exponential and logarithmic equations. Applications. \end{itemize} \bigskip \noindent {\bf Fine Details:} \begin{itemize} \item Chapter 2: ($\approx 10\; \%$) Know how to calculate the domain of composite function. Know how to determine if a function is 1-1. Know how to find the inverse of a 1-1 function. \vspace{-2mm} \item Chapter 3: ($\approx 45\; \%$) Be prepared to graph polynomials and rational functions without the help of a graphing calculator. Expect to solve arithmetical problems involving complex numbers. Know the geometrical interpretation of operations on complex numbers. Know the theorems concerning roots of polynomials. \vspace{-2mm} \item Chapter 4: ($\approx 45\; \%$) Know the definitions. Know the basic properties of exponential and logarithmic functions: domain and range, shape of curve, effect of base change. Know the laws of logarithms. Expect to solve exponential and logarithmic equations. Expect one or two ``applications'' involving compound interest or radioactive dating. In particular, know how to calculate half-life and estimate age given appropriate data. \end{itemize} \bigskip \noindent {\bf Practice:} \begin{itemize} \item Find the inverse of $f(x) = \frac{1-2x}{x-3}$. \vspace{-2mm} \item Explain why a 1-1 polynomial must have odd degree. Is every polynomial of odd degree 1-1? \vspace{-2mm} \item Graph $f(x) = \frac{2x^2(x-2)(x-4)^2}{(x-1)^2(x-3)^3}$. \vspace{-2mm} \item What are the domain and range of $f(x) = e^x + \ln(x)$? \vspace{-2mm} \item Solve $\log_2(x) + \log_3(x) + \log_4(x) = 1$ and $\log_x(2) + \log_x(3) + \log_x(4) = 1$. \vspace{-2mm} \item Three-fourths of a radioactive substance is lost due to decay over a 30,000 year period. What is the half-life of the substance? \end{itemize} \end{document}