Math 130 College Algebra, Spring 2008 NAME:____________

EXAM 2

7 problems, 10 points each

Instructions:

1. Show enough work to justify your answers.

2. Don't leave early unless you are sure you've solved all the problems.




  1. (1) Find the zeros of the function $f(x)=2x^{2}-x+3.$ Write the answers in the form $a+bi,$ where $a$ and $b$ are real numbers. (2) Simplify the following complex number: $i^{3}(1-2i)$. Write the answer in the form $a+bi,$ where $a$ and $b$ are real numbers$.$


  2. (1) Let $f(x)=3(x+1)^{2}.$ Plot of $y=x^{2}$ first then sketch the graph of $f$. What is the relation between the two? (2) The graph of $y=f(x)$ below is a parabola upside down. Its shape is exactly the same as that of $y=x^{2}.$ Find a formula for $f.$
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    MATH

  3. Solve the inequality $|2x+1|\geq 3$.


  4. Use the leading term test to describe the long term behavior of the function MATH
    MATH

  5. Find a polynomial of degree 3 with real coefficients and zeros: $0$ and $2+i.$


  6. Find the oblique asymptote of the function
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    MATH

  7. Let MATH. Find the multiplicities of the zeros of the numerator and the denominator of $f$ and use that information to sketch the graph of the function.

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