Asymptote Math Example 1

Solution

1. 1
   Vertical asymptote: set the denominator equal to zero. $x - 2 = 0 \Rightarrow x = 2$. Since the numerator $3(2)=6 \neq 0$, there is a vertical asymptote at $x = 2$.
2. 2
   Horizontal asymptote: compare degrees. Both numerator and denominator have degree $1$. Divide leading coefficients: $\frac{3}{1} = 3$. Thus the horizontal asymptote is $y = 3$.
3. 3
   Verify by taking the limit: $\lim_{x\to\infty}\frac{3x}{x-2} = \lim_{x\to\infty}\frac{3}{1-2/x} = 3$.