Find the horizontal and vertical asymptote

Question

For f(x)=5 (x+2)(2x-1)/ (4-x)(3x+2) The horizontal asymptote is at y = The vertical asymptote(s) is/are at =

Answer 1

Hi Jennifer,

 

Horizontal asymptotes are determined by the degree of the numerator and denominator.  Since both numerator and denominator are both quadratic (they both have 2 linear factors), the horizontal aymptote is located at the ratio of the leading coefficients.  If you expand the numerator, the leading term is 10x^2.  If you expand the denominator, the leading term is -3x^2.  This makes the horizontal asymptote the line y = -10/3

 

Vertical asymptotes are determined by setting the denominator equal to zero.  The denominator is zero when x = 4 and x = -2/3 so these lines are the vertical asymptotes.

 

Hope this helps.  :)