Vertical Asymptotes of Rational Functions

Question 1

Identify the vertical asymptote(s) of each function. Check all of the boxes that apply.

Revolt · Accepted Answer

x = 1; x = 2

Question 2

x = -16x = -4x = 0x = 4x = 16

Revolt · Accepted Answer

x = -4; x = 4

Question 3

Question 4

Revolt · Accepted Answer

x = −3: A; x = −2: B; x = 0: C; x = 2: D; x = 3: E; x = 5: F

Question 4

Which of the following statements are true of this rational function? Check all of the boxes that apply.

Revolt · Accepted Answer

There is a vertical asymptote at x = 0.; There is a removable discontinuity at x = –a

Question 5

Use the values in the table to find the value of R. R =

Revolt · Accepted Answer

8.31

Question 6

Use the inverse variation equation to fill in the table. p = 8.31 V Volume(Liters) Pressure(kilopascals) 83.1 a b 0.4 415.5 c

Revolt · Accepted Answer

2; 5; -3

Question 7

Use the equation where p = pressure and V = volume.What happens to the pressure as the volume approaches 0? Explain your reasoning.

Revolt · Accepted Answer

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.

Question 8

Question 10

Revolt · Accepted Answer

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.

Vertical Asymptotes of Rational Functions Answers

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