Mathematical Scratchpad

Extra Creidts (Due March 17, 2003)

  1. Suppose the graph of $f$ is given below. Then
    extra__2.png

    1. graph $y=-f(x),$

    2. graph $y=f(-x),$

    3. graph MATH

    4. graph MATH

  2. A company's profit function $P(x)$ (when $x$ number of units are produced) satisfies the following conditions:

    1. the profit function breaks even at $x=100,300$ and $500$ units

    2. the profit function $P(x)$ changes signs (from $P(x)>0$ to $P(x)<0$ or vise versa) at $x=100$ but $P(x)$ does not change sign at $x=300$ and $500.$

    3. $P(50)>0.$

      Then (a) find a profit function which satisfies all the conditions mentioned above. (b) Predict if 400 units is produced, would the company be profitable?

  3. Sketch the graph which you have found in question above$.$

  4. Find a rational function $f$ that satisfies ALL the following conditions:

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

    2. $f$ has a horizontal asymptote at $y=3.$

  5. page 170, number 4.

  6. page 171, number 32, (**find only horizontal and vertical asymptotes if they exist.)

  7. page 171, number 38 (**find only horizontal and vertical asymptotes if they exist.)

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