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

Answer:

1. The vertical asymptote: $x = 0$
2. The horizontal asymptote: $y = 0$
3. The domain: $(-\infty,0)\cup(0,\infty)$
4. The range: $(-\infty,0)\cup(0,\infty)$

Explanation:

Step1: Find vertical asymptote

Set denominator $x = 0$.

Step2: Find horizontal asymptote

As $x\to\pm\infty$, $\lim_{x\to\pm\infty}\frac{c}{x}=0$.

Step3: Find domain

Denominator cannot be 0, so $x\neq0$.

Step4: Find range

For $y = \frac{c}{x}$, $x=\frac{c}{y}$, $y\neq0$.