Question: Find the domain, intercepts, and asymptotes of f(x) when f(x)=(6(x)^2)+21x+15

Answer: Domain: x can be all real numbers

Intercepts: y-intercept exists when x=0, so it is (6(0)^2)+21(0)+15=15

x-intercept exists when y=0, so 0=(6(x)^2)+21x+15=3(2(x)^2)+7x+5)=3(2x+5)(x+1) Therefore, x-intercepts would be -5/2 and -1

Asymptotes: There are no vertical asymptotes

Also, no horizontal asymptotes.