Precalculus Practice Exam

Part 1 Test 1 Time: 1 hour


  1. Graph the function tex2html_wrap_inline111 and answer the following questions:

    Answers: The function is even, its four x-intercepts are at x=-3, x=-2, x=2 and x=3. The function is increasing on the intervals tex2html_wrap_inline127 and on tex2html_wrap_inline129 , the function is decreasing on the intervals tex2html_wrap_inline131 and on tex2html_wrap_inline133 . The maximum value is 36, attained at x=0; the minimum value is -6.25, attained at tex2html_wrap_inline137 .



  2. Let A=(3,1), B=(7,-4) , and C=(10,9).

    Answers: An equation of the circle is

    displaymath103

    The point C lies outside the circle.



  3. Let tex2html_wrap_inline153 and let tex2html_wrap_inline155 .

    Answers: The domain of f(x) is the interval tex2html_wrap_inline167 , the domain for g(x) is the interval tex2html_wrap_inline171 . Both functions will be invertible if their domain is further restricted to contain only non-negative numbers. The domain of tex2html_wrap_inline163 is the interval tex2html_wrap_inline175 .



  4. Solve for x in the following equation:

    displaymath104


    Answer: x = 2.



  5. Consider the algebraic expression

    displaymath105

    Find the domain of the expression and simplify the expression completely.


    Answers: The domain is the interval tex2html_wrap_inline181 . The expression can be simplified to

    displaymath106


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Thu Jun 12 22:29:17 MDT 1997

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