question 1 (1 point) which of the following is true? f(x)=1/(2 - x) has two vertical asymptotes. f(x)=1/x…

Answer:

1. B. $f(x)=\frac{1}{x}$ decreases over its entire domain.

Explanation:

Step1: Analyze $f(x)=\frac{1}{2 - x}$

The vertical - asymptote of $y = \frac{1}{2 - x}$ is found by setting the denominator equal to zero. So, $2−x = 0$, which gives $x = 2$. It has one vertical asymptote, not two.

Step2: Analyze $f(x)=\frac{1}{x}$

The domain of $y=\frac{1}{x}$ is $x\neq0$. Its derivative is $y'=-\frac{1}{x^{2}}<0$ for all $x$ in the domain $(-\infty,0)\cup(0,\infty)$. So it is decreasing over its entire domain.

Step3: Analyze $f(x)=-\frac{1}{x}$

When $x<0$, $y =-\frac{1}{x}>0$. So it is not always negative.

Step4: Analyze $f(x)=-\frac{1}{2x}$

Its derivative is $y'=\frac{1}{2x^{2}}>0$ for $x\neq0$. So it is increasing on $(-\infty,0)$ and $(0,\infty)$.