Vertical Asymptotes of Rational Functions Assignment

Identify whether each value of x is a discontinuity of the function by typing asymptote, hole, or neither. 5x/ x^3 + 5x^2 + 6x x = −3 x = −2 x = 0 x = 2 x = 3 x = 5

- asymptote -asymptote -hole -neither -neither -neither

The force of gravity between two objects is given by Fg = −Gm1m2/r2 , where G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between the objects' centers. Find the vertical asymptote of the graph of the function and explain its meaning in context.

An asymptote is 0 and it would make the graph increase to infinity as it approaches zero on the graph. In the equation, G represents the constant, and m1 and m2 are the masses, and r represents the distances.

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, the pressure will start to reach infinity.

The universal gas law, pV = nRT, describes the relationship among the pressure, volume, and temperature of a gas. p = pressure V = volume T = temperature (Kelvin) n = number of moles (quantity of gas particles) R = universal gas constant At a constant temperature of 1 K, the pressure and volume of 1 mole of gas vary inversely. Use the values in the table to find the value of R. Volume ------- Pressure 4. 155 ------- 2 16.62 ------- 0.5 33.24 ------- 0.25

R= 8. 31

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

a, b, and d a. f(x)= x -1/ x^2 -1 b. f(x)= x^2 -9/ x^2 +7x +12 d. f(x)= x +7/ x^2 +5x -14

Use the inverse variation equation to fill in the table. p = 8.31/ V Volume ------- Pressure 83.1 ------- a b ------- 0.4 415.5 ------- c

a= 0.1 b=20.775 c= 0.02

Which of the following statements are true of this rational function? Check all of the boxes that apply. f(x)= (x +a)(x +b)/ x^2 +ax

b and d b. There is a vertical asymptote at x = 0. d. There is a removable discontinuity at x = -a

Identify the vertical asymptote(s) of each function. Check all of the boxes that apply. f(x)= 3x/ x^2 -16

x= -4 x= 4

Identify the vertical asymptote(s) of each function. Check all of the boxes that apply. f(x)= x -8/ x^2 -3x +2

x=1 x=2