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

D: x = 1; E: x = 2

Question 2

Which functions have removable discontinuities (holes)? Check all of the boxes that apply.

Revolt · Accepted Answer

A: ; B: ; D:

Question 3

Question 3

Revolt · Accepted Answer

x = −3: asymptote; x = −2: is a zero of the denominator only; x = 0: is a zero of the numerator and denominator; x = 2: is a zero of the numerator only; x = 3: is a zero of the numerator only; x = 5: is a zero of the numerator only

Question 4

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

Revolt · Accepted Answer

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

Question 5

Use the values in the table to find the value of R. R = ⇒ 8.31

Revolt · Accepted Answer

PENDING

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

: 0.1; : PENDING; : PENDING

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 8

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.

Question 9

Did your answer include the following?

Revolt · Accepted Answer

AssessCtrl6fc7ff67-14fc-40a4-a888-d0fafd482146_1_A,AssessCtrl6fc7ff67-14fc-40a4-a888-d0fafd482146_1_B,AssessCtrl6fc7ff67-14fc-40a4-a888-d0fafd482146_1_C

Question 10

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

Revolt · Accepted Answer

B: x = -4; D: x = 4

Vertical Asymptotes of Rational Functions Answers

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