asymptote help

Question

Let f(x)= 2x-18

               x-5

a) state the domain

b) state the horizontal asymptote.

c) state the vertical asymptote(s). 

 

Answer 1

                2x-18
Let f(x)= -------
                  x-5

 

a) state the domain

 

All x (real numbers) except x = 5.  At x=5, the denominator =0 and division by 0 is undefined.

 

b) state the horizontal asymptote

 

The horizontal asymptote exists for large values of x.  As x gets very large, the "-18" term in the numerator and the "-5" term in the denominator become insignificant compared to the x values (picture x = 50 million), and f(x) approaches 2x/x = 2.  Thus the horizontal asymptote is y = 2.

 

c) state the vertical asymptote(s).

 

The vertical asymptote exists where the denominator goes to zero. Hence it exists at x=5