Practices for Polynomial functions

Math 145

  1. For MATH

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

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

    3. sketch the graph for f.

  2. For MATH

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

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

    3. sketch the graph for f.

  3. Find the revenue function, which is a quadratic function, satisfies ALL the function conditions:

    1. the company has no revenue when $x=100$ and $x=300$ units are produced.

    2. the maximum revenue is $\$40,000.$

  4. A company's profit function $P(x)$ (when $x$ number of units are produced) resembles a polynomial function and satisfies the following conditions:

    1. The profit function breaks even at $x=200,400$ and $600$ units.

    2. The profit function $P(x)$ changes signs (from $P(x)>0$ to $P(x)<0$ or vise versa) at $x=400$ but $P(x)$ does not change sign at $x=200$ and $600.$

    3. The company is profitable when $50$ units are produced.

      Then (a) find a profit function which satisfies all the conditions mentioned above. (b) Predict if 300 units is produced, would the company be profitable? (c) According to given information, when would the profit function reach a local maximum?

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

  6. For MATH

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

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

    3. sketch the graph for f.

  7. For $f(x)=2x^{2}+x+a$, 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.

  8. Explain why any even degree polynomial must have one y-intercept.

  9. Explain why any odd degree polynomial has at least one x-intercept.

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