graph all vertical and horizontal asymptotes of the rational function. f(x)=2x² + 6 / 2x + 5
graph all vertical and horizontal asymptotes of the rational function. f(x)=2x² + 6 / 2x + 5
Answer
Explanation:
Step1: Find vertical asymptote
Set denominator equal to 0. $2x + 5=0$ Solve for $x$: $x=-\frac{5}{2}$.
Step2: Find horizontal asymptote
Degree of numerator ($n = 2$) is greater than degree of denominator ($m = 1$). So, there is no horizontal asymptote. Instead, we have a slant asymptote. But we only focus on vertical and horizontal here.
Answer:
Vertical asymptote: $x =-\frac{5}{2}$, No horizontal asymptote.