graph all vertical and horizontal asymptotes of the rational function. f(x)=5/(-2x^2 + 2x + 12)

Explanation:

Step1: Find vertical asymptotes

Set the denominator equal to 0: $-2x^{2}+2x + 12=0$. Divide through by - 2 to get $x^{2}-x - 6=0$. Factor the quadratic: $(x - 3)(x+2)=0$. Solving gives $x = 3$ and $x=-2$. These are the vertical asymptotes.

Step2: Find horizontal asymptote

Degree of numerator is 0 and degree of denominator is 2. Since degree of numerator < degree of denominator, the horizontal asymptote is $y = 0$.

Answer:

Vertical asymptotes: $x = 3$ and $x=-2$; Horizontal asymptote: $y = 0$