Chapter 2.5, Problem 63E

(a)

To determine

Whether the statement “the graph of a function can never cross one of its horizontal asymptotes” is true or not.

(b)

To determine

Whether the statement “A rational function f has both $\underset{x\to \infty }{\lim }f\left(x\right)=L$ (where L is finite) and $\underset{x\to -\infty }{\lim }f\left(x\right)=\infty$” is true or not.

(c)

To determine

Whether the statement “the graph of the function can have any number of vertical asymptotes but at most two horizontal asymptotes” is true or not.

(d)

To determine

Whether the statement “$\underset{x\to \infty }{\lim }\left(x^3-x\right)=\underset{x\to \infty }{\lim }{x}^3-\underset{x\to \infty }{\lim }x=\infty -\infty =0$” is true or not.