Which power function does each of the following functions re

Which power function does each of the following functions resemble in the long-run? When x rightarrow plusminus infinity f(x) = 1/x approximately g(x) = 3x - 5/x - 2 approximately h(x) = x^2 + 1/x approximately r(x) = x^3 + 1/x approximately Sketch the graph of the respective asymptote \"curve\" for each of the functions above:

Solution

f(x) = 1/x ----> 0

Graph 1

g(x) = (3x-5)/(x -2) ---> 3x/x = 3

Graph 2

h(x) = (x^2 +1)/x ----> x

Graph 3

r(x) = (x^3 +x)/x ----> x^2

Graph 4