Mathematical Scratchpad

Additional Practices on Rational Functions

  1. Find two rational functions $f$ satisfying ALL the following conditions:

    1. $f$ has two vertical aysmptotes at $x=-1$ and $x=4$ respectively,

    2. $f$ has a horizontal aysmptote at $y=-3,$

    3. $f(0)=-3.$

  2. If MATH Then

    1. find the vertical asymptote(s) for $f,$

    2. find the horizontal asymptote for $f,$ if any.

  3. If MATH Then

    1. find the vertical asymptote(s) for $f,$

    2. find the horizontal asymptote for $f,$ if any.

    3. Assume you find a horizontal asymptote for $f$ above, say $y=a,$ determine what happens to the value of $y$ when MATH (Is $y\rightarrow a^{+}$ or MATH

  4. Suppose the average cost per unit for producing $x$ number of units for a manufacturing company is given by
    MATH

    1. If $12,000$ units are produced, find the average cost per unit.

    2. If MATH find the average cost per unit.

  5. Suppose the average profit per unit for selling $x$ number of units for a manufacturing company is given by
    MATH

    1. If $100,000$ units are produced, find the average profit per unit.

    2. If MATH find the average profit per unit.

  6. A manufacturing plant has determined that the cost $C$ (in dollars) of removing $x\%$ of the smokestack pollutants of its main smokestack is modeled by
    MATH

    1. What is the vertical asymptote of this function?

    2. What does the vertical asymptote mean to the plant owner?

    3. If the plant owner spends $200,000,$ how much pollutants can be removed?

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