Question

graphing multiples of a parent function
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 \( g(x)=\frac{f(x)}{h(x)} \), vertical asymptote occurs where \( h(x) = 0 \) (and \( f(x)
eq0 \) there). For \( g(x)=\frac{10}{x} \), \( h(x)=x \). Set \( x = 0 \), and \( 10
eq0 \) at \( x = 0 \), so vertical asymptote is \( x = 0 \).

Step2: Find horizontal asymptote

For rational functions \( \frac{ax^n}{bx^m} \), if \( n=m \), horizontal asymptote is \( y=\frac{a}{b} \); if \( nm \), no horizontal asymptote. Here, \( g(x)=\frac{10}{x}=\frac{10x^0}{x^1} \), \( n = 0 \), \( m = 1 \), \( n

Answer:

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