How do you find the asymptotes for #f(x) = (x+1) / (x^2 +3x - 4) #?

1 Answer
Jan 25, 2016

Answer:

#x=-4# and #x=+1#

Explanation:

Vertical asymptotes
substitute values of x that will make the denominator 0.
to do that you must factor, the denominator to obtain
#color(white)("XX") (x+4)(x-1)#,
then the values that would make this denominator 0 are
#color(white)("XX") -4 and +1#.

therefore, the equations of the asymptotes are,
#color(white)("XX") x=-4 and x=1#.
graph{(x+1)/(x^2+3x-4) [-6.244, 6.243, -3.12, 3.123]}

Note there are no horizontal asymptotes.