Chapter 2, Problem 5RCC

(a)

To determine

To Describe: The line $x=a$ is a vertical asymptote of the curve $y=f\left(x\right)$.

Explanation of Solution

The vertical asymptote of the function $y=f\left(x\right)$ is $x=a$, if y approaches $\pm \infty$ as x approaches a from the right or left.

Limit is defined as $\underset{x\to a^{-}}{\lim }f\left(x\right)=\pm \infty$ (or) $\underset{x\to a^{+}}{\lim }f\left(x\right)=\pm \infty$ (or) both

Graph:

(b)

To determine

To Describe: The line $y=b$ is a horizontal asymptote of the curve $y=f\left(x\right)$.

Explanation of Solution

The horizontal asymptote of the function $y=f\left(x\right)$ is $y=b$, if y approaches b as x approaches to $\pm \infty$.

Limit is defined as $\underset{x\to -\infty }{\lim }f\left(x\right)=b$ (or) $\underset{x\to +\infty }{\lim }f\left(x\right)=b$(or) both

Graph: