`f(x)=(x^2-9)/(2x^2+1)` Graph the function.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

We are asked to graph the function ` y=(x^2-9)/(2x^2+1) ` :

Note that the denominator is always positive so there are no vertical asymptotes. (The domain is all real numbers.)

The numerator factors as (x+3)(x-3), so the x-intercepts are at -3 and 3. For x<-3 the numerator is positive so the function is positive; for -3<x<3 the numerator is negative, and for x>3 the numerator is positive.

Since the degree of the numerator is the same as the degree of the denominator, there is a horizontal asymptote at y=1/2.

If you have calculus, the first derivative is `(38x)/((2x^2+1)^2) ` . The function is decreasing on x<0 and increasing on x>0 and has a global minimum at (0,-9).

The graph:

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial