Question

consider the function $g(x) = \frac{10}{x}$. the vertical asymptote is $x = \square$. the horizontal asymptote is $y = \square$.

Explanation:

Step1: Find vertical asymptote

For a rational function \(y = \frac{a}{x - h}+k\) (in this case \(a = 10\), \(h = 0\), \(k=0\)), the vertical asymptote occurs where the denominator is zero. Set \(x=0\), so the vertical asymptote is \(x = 0\).

Step2: Find horizontal asymptote

For a rational function \(y=\frac{n}{x}\) (where \(n\) is a non - zero constant), as \(|x|\to\infty\), \(\lim_{x
ightarrow\pm\infty}\frac{10}{x}=0\). So the horizontal asymptote is \(y = 0\).

Answer:

The vertical asymptote is \(x = 0\). The horizontal asymptote is \(y = 0\).