asymptotes

Question

Find the vertical, horizontal, and oblique asymptotes, if any, for the given rational function. R(x) 10x^2+3x-18 /2x+3?

 

 

Answer 1

R(x) = (10x²+3x-18)/(2x+3)

 

        = [(2x+3)(5x-6)]/(2x+3)

 

         = 5x-6 , for all x ≠ -3/2

 

The graph of y = R(x) is the same as the graph of y = 5x-6 except for a "hole" in the graph when x = -3/2.  

 

So, the graph of y = R(x) is the line with slope 5 and y-intercept (0,-6) and which has a hole at (-3/2, -13.5).  

 

There are NO asymptotes.

 

Answer 2

See the answer by Mark M.