Let fx x2 2x 153x2 12x 15 Find the equations of the hori

Let f(x) x^2 + 2x - 15/3x^2 + 12x - 15. Find the equations of the horizontal asymptotes and the vertical asymptotes of f(x). If there are no asymptotes of a given type, enter NONE. If there is more than one asymptote of a given type, give a comma separated list (i.e.: 1, 2....). Horizontal asymptotes: y = Vertical Asymptotes: x =

Solution

f(x) = ( x^2 + 2x - 15 ) / (3x^2 + 12x - 15 )

when the degree of numerator = degree of denominator in a rational function

the horizontal asymptote is given by leading coefficient of numerator / leading coefficient of denominator

y = 1 / 3

to find vertical asymptote set denominator equal to zero and solve for x

3x^2 + 12x - 15 = 0

x^2 + 4x - 5 = 0

( x + 5 ) ( x- 1) = 0

x = 1

vertical asymptote is x = 1