Question 1140197
i chose (x^2 + x - 19) / (x^2 + x - 20).


here's my graph:


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x^2 + x - 20 factors out to be (x+5) * (x-4), creating the vertical asymptotes at x = -5 and x = 4.


the horizontal asymptote is as y = 1 because, as positive values of x get larger and larger, and negative values of x get larger and larger, the difference between the numerator and the denominator becomes smaller and smaller, eventually leading to a result that gets closer and closer to 1 but never quite becoming 1 no matter how large the value of x becomes.


the following excel spreadsheet shows the calculations that result in the vertical asymptotes at x = -5 and x = 4, and result in the horizontal asymptotes as plus or minus x gets larger and larger.


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