Write a rational function f that has the specified characteristics. (There are many correct answers.) (a) Vertical asymptote: x = 1 Horizontal asymptote: y = 0

Question

need help to solve

Answer 1

f(x) = (x - 1) / (x² - 1)             is one example.

 

If you plug in x=1 into the function, you make the denominator equal to zero.  Also, the degree of the numerator is less than the degree of the denominator.  When this happens, the horizontal asymptote is always y=0.

 

There is another, as you said.  Use the information I have given you to find more.

Answer 2

Vertical Asymptote at x=1 if denominator = 0 when x = 1 but the numerator ≠ 0 when x = 1.  Horizontal asymptote at y = 0 if the degree of the denominator is larger than the degree of the numerator.  

 

Example:  f(x) = (x+1)/(x-1)²