Math 130 College Algebra, Spring 2008 NAME:____________


7 problems, 10 points each


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 $f.$


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

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

  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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