Problema Solution
Let f(x) = (3x^2-17x+20)/(3x^2+17x+20)
This function has:
1) A y intercept at y=
2) Roots at A and B, where A < B
3) Vertical asymptotes at C and D, where C < D
4) Horizontal asymptote at y =
Answer provided by our tutors
first thing we need to do is factor this function, giving us the roots and y-intercepts
we factor the numerator:
(3x^2-17x+20) = (x-4)(3x-5)
we factor the denominator:
(3x^2+17x+20) = x(3x+5)+4(3x+5) = (3x+5)(x+4)
y = 0 when the numerator equals zero, so we have y-intercepts at:
(x-4)=0, or x=4
(3x-5)=0, or x=5/3
to find vertical asymptotes we want to solve for when the denominator equals zero:
(3x+5) = 0, or x=-5/3
(x+4) = 0, or x=-4
there is a horizontal asymptote at y=1 which we determine by nothing the dominant terms in the numerator and denominator:
3x^2 / 3x^2 = 1