Consider the function [tex]\( g(x) = \frac{10}{x} \)[/tex].
To determine the vertical asymptote, we need to identify the value of [tex]\( x \)[/tex] that makes the denominator zero. This occurs when:
[tex]\[ x = 0 \][/tex]
So, the vertical asymptote is at [tex]\( x = 0 \)[/tex].
For the horizontal asymptote, we examine the behavior of [tex]\( g(x) \)[/tex] as [tex]\( x \)[/tex] approaches infinity or negative infinity. Since the degree of the numerator (which is 0) is less than the degree of the denominator (which is 1), the horizontal asymptote is:
[tex]\[ y = 0 \][/tex]
Therefore, the vertical asymptote is [tex]\( x = 0 \)[/tex] and the horizontal asymptote is [tex]\( y = 0 \)[/tex].
