Math Questions and Answers

Start Your Free Trial

State the asymptotes, holes, roots and intercepts for 2x^2+10x+12/x^2-9 Include Vertical asymptote, horizontal asymptote, roots, x-int and y-int with end behaviours and describe how the graph will look like 

Expert Answers info

beckden eNotes educator | Certified Educator

calendarEducator since 2011

write562 answers

starTop subjects are Math, Science, and Business


We can factor to get


We can simplify with the idea that x!=-3 or x!=3


Now we have vertical asymptotes at x=3, and a hole at x=-3.

Since deg(2(x+2)) = deg(x-3) and the leading coefficients are 2 and 1 we get a horizontal asymptote at y=2.

The x-intercept is when 2(x+2) = 0 or x=-2.

The y-intercept is when y=(2(0+2))/(0-3)=-4/3

The end behavior is y=2.

The below graph is how we would plot this funcion:

Note the hole at x=-3, it is not an asymptote.


check Approved by eNotes Editorial

Sylvia Pfeffer eNotes educator | Certified Educator

calendarEducator since 2012

write301 answers

starTop subject is Math




1) Since x=3, and x=-3 get the denominator to be zero than they are your certical asymptote.

2) Since the numerator and denominator are of the same degree we have a horizontal asymptote, y=2.

3) No oblique asymptote.

4) Roots



Hence x-intercept (-2,0)

5) y-intercept








check Approved by eNotes Editorial