consider the function $f(x)=\frac{c}{x}$, where $c$ is a nonzero real number.\nthe vertical asymptote\nthe…

Explanation:

Step1: Find vertical asymptote

The function $f(x)=\frac{c}{x}$ is undefined when $x = 0$. As $x$ approaches $0$ from either side, the function values tend to positive or negative infinity. So the vertical asymptote is $x = 0$.

Step2: Find horizontal asymptote

As $x\to\pm\infty$, $\lim_{x\to\pm\infty}\frac{c}{x}=0$. So the horizontal asymptote is $y = 0$.

Step3: Find domain

The function $f(x)=\frac{c}{x}$ is defined for all real - numbers except $x = 0$. So the domain is $(-\infty,0)\cup(0,\infty)$.

Step4: Find range

Let $y=\frac{c}{x}$, then $x=\frac{c}{y}$. This is undefined when $y = 0$. So the range is $(-\infty,0)\cup(0,\infty)$.

Answer:

Vertical asymptote: $x = 0$ Horizontal asymptote: $y = 0$ Domain: $(-\infty,0)\cup(0,\infty)$ Range: $(-\infty,0)\cup(0,\infty)$