Question 1196677
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x = number of items made and sold


P = profit = 5x-20 = 5(x-4)
negative profit means the company has lost money; positive is when the company makes money


Let's say the company has sold x^2-x-12 items


average profit = (profit)/(number of items sold)
average profit = (5x-20)/(x^2-x-12)
average profit = 5(x-4)/( (x+3)(x-4) )
average profit = 5/(x+3)


This curve produces a vertical asymptote at x = -3 due to the division by zero error. Plugging x = -3 into the function causes the x+3 to become zero.


The (x-4) terms cancel, so we don't have a vertical asymptote at x = 4. But we have a hole here because the original un-simplified version will be used when calculating points to graph out. 


Other ideas for rational functions could be:<ul><li>The ratio of one chemical solution to another</li><li>Rate = distance/time</li></ul>
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