consider the function f(x)=c/x where c is a nonzero real number. the vertical asymptote the horizontal…

Explanation:

Step1: Find vertical - asymptote

For the function $f(x)=\frac{c}{x}$, when the denominator $x = 0$, the function is undefined. As $x$ approaches $0$ from the left or right, the function values approach positive or negative infinity. So the vertical asymptote is $x = 0$.

Step2: Find horizontal - asymptote

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

Step3: Find domain

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

Step4: Find range

As $x$ varies over its domain, $y=\frac{c}{x}$ can take any non - zero real value. As $x\rightarrow\pm\infty$, $y\rightarrow0$ but $y\neq0$. So the range is all real numbers except $y = 0$, or $(-\infty,0)\cup(0,\infty)$.

Answer:

The vertical asymptote: $x = 0$ The horizontal asymptote: $y = 0$ The domain: All real numbers except $x = 0$ The range: All real numbers except $y = 0$