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{\large\bf Information for Test 2}

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{\bf Office Hrs:} Extra (R: 1:30-2:30), Usual (R: 4-6).

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{\bf Calculator:} OK. (But the use of a graphing calculator 
may be restricted on some problems.)

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{\bf Advice:} Look over old quizzes and HW problems.
If you missed points on a problem, know why you missed them!

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{\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}

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{\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}

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\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}

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{\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}

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