graph all vertical and horizontal asymptotes of the rational function. f(x)=(2x^2 + 6)/(2x + 5)

Explanation:

Step1: Find vertical asymptote

Set denominator equal to 0. $2x + 5=0$ Solve for $x$: $2x=-5$ $x =-\frac{5}{2}$

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 can find the slant asymptote by long - division. But since the question asks only for vertical and horizontal asymptotes, we focus on the vertical one found above.

Answer:

Vertical asymptote: $x =-\frac{5}{2}$, No horizontal asymptote.