Vertical Asymptotes of Rational Functions

Question 1

Identify the vertical asymptote(s) of each function. Check all of the boxes that apply.x = -8x = -2x = -1x = 1x = 2x = 8

Revolt · Accepted Answer

x = 1; x = 2

Question 2

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

Revolt · Accepted Answer

x = -4; x = 4

Question 3

x = 0 [___]

Revolt · Accepted Answer

x = 0: hole; x = 2: neither; x = 3: neither; x = 5: PENDING; hole

Question 4

x = 2 [___]

Revolt · Accepted Answer

x = 2: neither; x = 3: neither; x = 5: PENDING; neither

Question 5

x = 3 [___]

Revolt · Accepted Answer

x = 3: neither; x = 5: PENDING; neither

Question 6

x = 5 [___]

Revolt · Accepted Answer

neither

Question 7

x = −3

Revolt · Accepted Answer

x = −3: asymptote

Question 8

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

Revolt · Accepted Answer

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

Question 9

⇒ 0.1

Revolt · Accepted Answer

20.775; 0.02; 0.1

Question 10

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.

Vertical Asymptotes of Rational Functions Answers

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