Determine the vertical asymptotes of the function fx x32x29

Determine the vertical asymptote(s) of the function f(x) = x-3/2x^2-9x-5

Solution

Vertical asymptote of the function :

For rational functions the vertical asymptotes are the undefined points , also known as the zeros of the denominator.

So that to find the vertical asymptotes we set the denominator of the function f(x) = ( x - 3 ) / ( 2x² - 9x - 5 )

to zero . That is 2x² - 9x - 5 = 0 implies that x = - 1/2 and x = 5

     Therefore, the vertical asymptotes of the function f(x) = ( x - 3 ) / ( 2x² - 9x - 5 ) are x = - 1/2 and x = 5