Question

consider the function $f(x) = \frac{c}{x}$, where $c$ is a nonzero real number.
the vertical asymptote is $x = 0$
the horizontal asymptote is $y = 0$
the domain
the range
done
cannot be determined
is all nonzero real numbers
is all real numbers except $c$
is all real numbers

Explanation:

Step1: Analyze the domain

For the function \(y = \frac{c}{x}\), the denominator cannot be zero. When \(x = 0\), the function is undefined. So the domain is all real numbers except \(x = 0\).

Step2: Analyze the range

Let \(y=\frac{c}{x}\), then we can solve for \(x\) as \(x=\frac{c}{y}\). The denominator \(y\) cannot be zero. So the range is all non - zero real numbers.

Answer:

The domain is all real numbers except \(x = 0\). The range is all non - zero real numbers.