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\leftline{\bf  Math 135 - section 01 -  Precalculus Diagnostic Quiz}
\leftline{\bf  September 6,  2019}
\vspace{.2in}
\leftline{Your Name:$\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$}

\vspace{.2in}
\noindent
{\bf Show your work}.  Circle the correct answer in the multiple choice questions.
 Please turn over for problems 4,5,6.
\begin{enumerate}

\item Find all real numbers $x$ satisfying $|2x - 6| = 8$. \vspace{2.5in}


\item Solve for $t$:  \ \ $3t^2 - 4t + 1 = 0$ (find all real number solutions). \vspace{2.5in} 


\item Which simplified form is equal to 
$$\displaystyle \left(u^{-6}v^2 \right)^3 \cdot \left(\frac{v^{-2}}{u^2}\right)^{-1}?$$\vspace{.1in}

A. \ $u^{-16}v^8$ \ \ \ \ \ B. \ $u^{-14}v^{4}$ \ \ \ \ \ C. \ $u^{-9}v^{3}$ \ \ \ \ \ D. \ $(uv)^{-7}$ \vspace{1.8in}

\vfill\eject

\item Find common factors and cancel to simplify: 
$\displaystyle \frac{12 x}{5x-10} \cdot \frac{x^2-4}{2x+4}$\vspace{.1in}

A. \ $\displaystyle \frac{x^2+12x-4}{5x-2}$ \ \ \ \ B. \ $\displaystyle \frac{6x}{5}$ \ \ \ \ C. \ $\displaystyle -\frac{4}{3}(x-1)$ \ \ \ \ D. \ $\displaystyle \frac{6x^2 + 12}{5x + 10}$ \ \ \ \ E. 
None of the above.\vspace{1.8in}


\item If $f(x) = 5x^2-11$, find $f(a+1) - f(a)$ and simplify. \vspace{2.5in}


\item Let $f(x) = x^2 - 3 x$ and $g(x) = x + 1$.  Which function is equal to $f(g(x))$?

A.  $x^2 - x$\ \ \ \ \ B. $x^2 - 3x + 1$\ \ \ \ \ \ C. $x^2 + x$\ \ \ \ \ D. $x^2 - x - 2$
\vspace{1.8in}

\end{enumerate}

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