Vertical Asymptotes of Rational Functions Answers
Which of the following statements are true of this rational function? Check all of the boxes that apply.There is a removable discontinuity at x = –b.There is a vertical asymptote at x = 0.There are no removable discontinuities.There is a vertical asymptote at x = –a.There is a removable discontinuity at x = –a
a = [___], b = [___], c = [___]
a = 0.1, b = 20.775, c = 0.02
a = [___], b = [___], c = [___]
a = 0.1, b = 20.775, c = 0.02
⇒ 0.1
0.1
Use the equation where p = pressure and V = volume.What happens to the pressure as the volume approaches 0? Explain your reasoning.
As the volume approaches 0, the pressure approaches infinity. This is because the equation p = 8.31 / V is a rational function that is undefined at V = 0, creating a vertical asymptote. As the denominator (V) gets smaller and smaller, the resulting pressure (p) increases without bound.
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The gravitational force function, F = G(m1m2/r^2), has a vertical asymptote at r = 0 because the denominator is zero when r = 0. This indicates that as the distance (r) between two objects approaches zero, the gravitational force (F) between them approaches infinity.
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Which of the following statements are true of this rational function? Check all of the boxes that apply.
Which did you include in your answer?The pressure approaches infinity.The function is undefined for V = 0.There is an asymptote at V = 0.
Did your answer include the following?Examine the denominator and find that r2 = 0 when r = 0.Determine that there is a vertical asymptote at r = 0.Conclude that as the distance between the objects approaches 0, the gravitational force between them approaches infinity.
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