updated-pset-2-RMD.Rmd

---
title: "Problem Set 2"
author: "NAME"
date: "DATE"
output: pdf_document
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\maketitle

Due start of class on Day 5. 

\begin{enumerate}
    \item Exponents and Logarithms
        \begin{enumerate}
            \item Multiply $x^4 y^3 z^2 (1 + x^2 y^2)$
            \item Simplify $((xy)^{-6})^{0.5} y^3z^{3}$
            \item Simplify $((xy)^2)^{1.5} x^{-3}y^{-3}$
            \item Solve $ln(e^5/e^{2.5})$
            \item Simplify $e^{ln 7.14}$
            \item What is $log_{7134\pi}(1)$?
            \item Solve for x $log_x(16)=4$ 
            \item Combine into one term: $log(3x)+2log(y)$ 
        \end{enumerate}

    \item Inequalities and Absolute Values
        \begin{enumerate}
            \item ``Solve'' for $x$: $x + y +2 < 4$
            \item ``Solve'' for $x$: $(-4)(x + 7) \geq -24$
            \item What is the absolute value of $-24$?
            \item Graph $y = x^2$ and $y=x^3$ 
        \end{enumerate}

    \item Factor
        \begin{enumerate}
            \item $x^2+ 5x+4$
            \item $6m^2+8m-8$ 
            \item $5y^2-12yz+7z^2$ 
        \end{enumerate}

    \item Functions
        \begin{enumerate}
            \item What is the difference between a function and relation (in words)?
            \item Simplify $h(x)=g(f(x))$, where $f(x)=x^2+4$ and $g(x)=\sqrt{x-4}$ 
            \item Find the inverse function of $f(x)=5x-3$ 
            \item What is a quadratic function? (define and provide example) 
            \item Why do we care if a function is monotonically doing anything?
        \end{enumerate}

    \item Exponent(ials)
        Explain the difference between, and provide an example of, the following. Be sure to use an example different from the slides: 
            \begin{enumerate}
                \item Exponent:
                \item Exponential:
                \item Exponential Function: 
            \end{enumerate}

    \item Matrices:
            \begin{enumerate}
                \item Add these two matrices: $
                    \begin{bmatrix}
                        2 & 4 & 2 \\
                        1 & 4 & 0 \\
                        2 & 6 & 0
                    \end{bmatrix}
                        +
                     \begin{bmatrix}
                     5 & 1 & 1 \\
                     2 & 2 & 2\\
                     4 & 1 & 3
                     \end{bmatrix}$


        \item Multiply these two matrices: $
                    \begin{bmatrix}
                        2 & 4 & 2 \\
                        1 & 4 & 0 \\
                        2 & 6 & 0
                    \end{bmatrix}
                    *
                    \begin{bmatrix}
                        5 & 1 & 1 \\
                        2 & 2 & 2 \\
                        4 & 1 & 3
                    \end{bmatrix}
                    $
            \item Provide an example matrix, showing what happens when you multiply by the identity matrix. 
        \end{enumerate}


\item Topics and Questions
    \begin{enumerate}
        \item List three things you struggled with on today's assignment. 
        \item What is your plan for improving the items listed above?
        \item What percent of the material was new to you today?
        \item What is one new concept you learned today?
        \item What question do you still have about the material?
    \end{enumerate}


\end{enumerate}