Vertical Asymptotes of Rational Functions Answers
Identify the vertical asymptote(s) of each function. Check all of the boxes that apply.x = -8x = -2x = -1x = 1x = 2x = 8
x = -16x = -4x = 0x = 4x = 16
x = 0 [___]
hole
x = 2 [___]
neither
x = 3 [___]
neither
x = 5 [___]
neither
Which functions have removable discontinuities (holes)? Check all of the boxes that apply.
Question text not available
x = −3
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
⇒ 0.1
0.1
Identify the vertical asymptote(s) of each function. Check all of the boxes that apply.
Which functions have removable discontinuities (holes)? Check all of the boxes that apply.
Question text not available
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
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 from above, the pressure approaches infinity. The function is undefined at V = 0, which is a vertical asymptote.
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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.
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