Find the intercepts and asymptotes

Question

a) r(x) = x − 2 / x² − 4x

 

 

b) s(x) = x² − 2x + 1 / x³ − 3x²

Answer 1

Factor r(x) completely.

 

r(x) = (x - 2) / (x² - 4x)

 

r(x) = (x - 2) / [x(x - 4)]

 

 

Set r(x) equal to zero.

 

0 = (x - 2) / (x(x - 4))

 

 

To find the zeros, set the denominator equal to zero and solve for x.  To find the vertical asymptotes, set the denominator equal zero and solve for x.

 

 

Try the last one on your own.