1. The graphs of the two equations $\displaystyle y=-3\,x-{{3}\over{4}}$ and $\displaystyle y=3\,x^2$ intersect in how many distinct points?

    none

    unknown

    two

    one

    three

  2. Which of the following is the domain of $f(x)=\sqrt{x^2 - 36 }$?

    $(-\infty, 6 ]$

    $\left\{x \,\left\vert\, \vert x\vert \ge 6 , \,\mbox{$x$\ is a real number} \right.\right\}$

    $(-\infty,\infty)$

    $\left\{x \,\left\vert -6 \leq x \leq 6 , \,\mbox{$x$\ is a real number} \right.\right\}$

    $[ -6 ,\infty)$

  3. $\log_{ 7} \left(\displaystyle 49 \right)$ =

    2

    $\displaystyle {{1}\over{2}}$

    7

    −2

    −7

  4. If $\displaystyle t=e^{x-5}$ then $x=$

    $\displaystyle \ln t$

    $\displaystyle {{t-2}\over{e}}$

    $\displaystyle \ln t+5$

    10

    −10

  5. The polynomial equation $\displaystyle x\,\left(x^2-4\right)\,\left(x^2-3\right)=0$ has how many real roots?

    two only

    three only

    only one

    four only

    five

  6. Of the following, which best represents the graph beside?

    Image part3_pick_plot0

    $\displaystyle y=\ln x$

    $\displaystyle y=1-x^2$

    $\displaystyle y=e^ {- x }$

    y = 1 − x

    $\displaystyle y=\sqrt{x-1}$


Department of Mathematics
Last modified: 2026-01-20