Consider the rational function 2/(25-x^2)

Question

A) How does the function behave as x approaches positive/ negative infinity?  

B) Does the function have any symmetry?  

C) Find and classify the critical points  

D) Find the points of inflection and the intervals of concavity. 

E) State the equation of the asymptotes

Answer 1

The easiest way to answer this question is to graph the function.

It has a minimum point at x = 0.

It has non-removable jump discontinuities at x = 5 and x = -5 where it "blows up".

It is asymptotic to y = 0 as x becomes large in either direction.