Review for test 2

  1. Find the profit function, which is a quadratic function, satisfies ALL the function conditions:

    1. the break even units for this profit function is at $x=50$ and $x=150. $

    2. the maximum profit is $\$10,000.$

  2. Find a polynomial $f$ satisfies the following conditions:

    1. $f$ has repeated $x-interecepts$ (even number of times) at $x=-1$ and $x=3;$

    2. $f$ has non-repeated $x-intercepts$ at $x=-2$ and $x=4.$

    3. $f(-5)<0.$

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

  4. Find a polynomial $f$ satisfies the following conditions:

    1. $f$ has repeated (even number of times) $x-interecepts$ at $x=3;$

    2. $f$ has repeated (odd number of times) $x-intercepts$ at $x=1$ and $x=4.$

    3. $f(5)<0.$

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

  6. Find the profit function, which is a quadratic function and satisfies ALL the following conditions: (a) the company breaks even when $x=100$ and $x=300$ units are produced, (b) the maximum revenue is $\$40,000.$

    1. MATH

    2. MATH

    3. MATH

    4. MATH (correct).

    5. None of above.

  7. Find a profit function $P(x)$ satisfies ALL the following conditions, where $x$ denotes number of units are produced and $P(x)$ is a polynomial function: (a) the company breaks even at $x=100,300$ and $500$ units (b) 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 $500,$ (c) the company is not profitable when $50$ units are produced.

  8. For MATH

    1. find the $x-intercepts$ of $f,$

    2. find the interval(s) where $f(x)>0,$

    3. sketch the graph for f.

  9. For $f(x)=2x^{2}+ax+4$, then

    1. find $a$ so that the graph of $y=f(x)$ has exactly one x-intercept,

    2. find $a$ so that the graph of $y=f(x)$ has two x-intercepts,

    3. find $a$ so that the graph of $y=f(x)$ has no x-intercept.

  10. If $f(x)=x^{2}-4x+1.$Then

    1. find the vertex of $f,$

    2. find the $y-intercept$ of $f,$

    3. find hte line of symmetry of $f,$

    4. sketch $f.$

  11. True or False:

    1. Any odd degree polynomail has at least one x-intercept.

    2. Any even degree polynomail has at least one x-intercept.

    3. The function MATH has no $x-intercept$ in the interval of [0, 1].

    4. For a degree four polynomial, MATH the number $e$ will affect the graph of $y=f(x)$ in horizontal direction.

  12. Let $f$ be the function graphed below:
    reviewtest2__68.png

    1. Does $f$ have an inverse in the domain of $[-4,4]?$ Explain.

    2. If we restrict the domain of $f$ to be $[-2,2],$ does $f^{-1}$ exist? Explain.

    3. If $f(-2)=-1,$ $f(-1)=-3$ and $f(2)=-7,$ find $f^{-1}(-1),$ $f^{-1}(-3)$ and $f^{-1}(-7).$

  13. If MATH

    1. Then determine if $f$ has an inverse? explain.

    2. If $f^{-1}$ exists, find $f^{-1}.$

    3. Verify if MATH

    4. Graph $f$, and $f^{-1}$ together.

  14. If $f(x)=2x^{2}-4,$ $x<0.$

    1. Find $f^{-1}$ if it exists.

    2. Sketch $f^{-1}$ and $f$ together if $f^{-1}$ exists.

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