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

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Revolt · Accepted Answer

x = -4; x = 4

Question 3

x = −3 x = −2 x = 0 x = 2 x = 3 x = 5

Revolt · Accepted Answer

x = −3: asymptote; x = −2: asymptote; x = 0: hole; x = 2: neither; x = 3: neither; x = 5: neither

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

a = ⇒ 0.1, b = ⇒ 20.775, c = ⇒ 0.02

Revolt · Accepted Answer

⇒ 0.1: 2; ⇒ 20.775: a = 0.1, b = 20.775, c = 0.02; ⇒ 0.02: a = 0.1, b = 20.775, c = 0.02

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 (V) approaches 0, the pressure (p) approaches infinity. This occurs because the variable V is in the denominator of the equation p = 8.31/V. As the denominator gets smaller and closer to 0, the overall value of the fraction increases without bound. Mathematically, there is a vertical asymptote at V = 0, and the function is undefined at that specific point since division by zero is impossible.

Question 8

Question 14

Revolt · Accepted Answer

To find the vertical asymptote of the gravitational force function, we examine the denominator, r^2. Setting the denominator to zero (r^2 = 0) shows that there is a vertical asymptote at r = 0. This means that as the distance (r) between two objects approaches zero, the gravitational force between them increases without bound, approaching infinity.

Vertical Asymptotes of Rational Functions Answers

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