Question

graphing asymptotes for a rational functions
two copies of the same rational function are shown below
on the graph below draw the horizontal asymptote and write the equation for the horizontal asymptote underneath.
$f(x)=\frac{-2}{x + 2}$
clear all draw
horizontal asymptate:
on graph below, draw the the vertical asymptote and write the equation for the vertical asymptote underneath.
$f(x)=\frac{-2}{x + 2}$
clear all draw:
vertical assmptote:

Explanation:

Step1: Find horizontal asymptote

For a rational function \(y=\frac{f(x)}{g(x)}\) where \(f(x)=- 2\) (degree \(0\)) and \(g(x)=x + 2\) (degree \(1\)). When the degree of the numerator \(n\) is less than the degree of the denominator \(m\) (\(n=0,m = 1\)), the horizontal asymptote is \(y = 0\).

Step2: Find vertical asymptote

Set the denominator equal to zero. For \(g(x)=x + 2\), solve \(x+2=0\). Subtracting \(2\) from both sides gives \(x=-2\). So the vertical asymptote is \(x =-2\).

Answer:

Horizontal Asymptote: \(y = 0\)
Vertical Asymptote: \(x=-2\)