1.9.3 quiz: finding vertical asymptotes for the function f(x) = 1/(x + 1), which of these could be a value…

Explanation:

Step1: Analyze the function near x = - 1

The function is $F(x)=\frac{x}{x + 1}$. As $x$ approaches - 1 from the left side ($x\to - 1^{-}$), let $x=-1 - h$ where $h>0$ and $h\to0$. Then $F(x)=\frac{-1 - h}{-1 - h+1}=\frac{-1 - h}{-h}=\frac{1 + h}{h}=\frac{1}{h}+1$. As $h\to0$, $F(x)\to+\infty$. As $x$ approaches - 1 from the right side ($x\to - 1^{+}$), let $x=-1 + h$ where $h>0$ and $h\to0$. Then $F(x)=\frac{-1 + h}{-1 + h+1}=\frac{-1 + h}{h}=\frac{-1}{h}+1$. As $h\to0$, $F(x)\to-\infty$. So when $x$ is close to - 1, the function value can be a very large - magnitude negative number.

Answer:

C. -10,000