SOLUTION: Create a real-life word problem an rational function with a vertical asymptote at x=-3 and a hole at x=4.

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Question 1196677: Create a real-life word problem an rational function with a vertical asymptote at x=-3 and a hole at x=4.
Found 3 solutions by josgarithmetic, ikleyn, math_tutor2020:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
A rational function, doable.
As a real-life problem? Too many possibilities which really depend on YOU.

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

Below is my real-life problem:


        "a teacher assigned to pupils to plot a graph of a rational function
        with vertical asymptote at x= -3 and a hole at x= 4."



Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

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:
  • The ratio of one chemical solution to another
  • Rate = distance/time