Question

State the horizontal asymptote of the rational function. (5 points) worth lots of points!!!

f(x) = quantity three x squared minus four x minus three divided by quantity two x squared minus three x plus two

Answer 1

f(x) = (x^2 + x - 2) / (x^2 - 3x - 4)

Domain is all real numbers except the valus of x for which x^2 - 3x - 4 = 0

(x + 1)(x - 4) = 0

x = -1, x = 4

Domain is all real numbers except x = -1 and x = 4. (-∞, -1) ∪ (-1, 4) ∪ (4, ∞)

Range is all real numbers

x-intercepts are the values of x for which x^2 + x - 2 = 0

(x - 1)(x + 2) = 0

x = 1, x = -2

x-intercepts are x = 1 and x = -2

y-intercept is y = 1/2

It has no Horizontal asymptotes

Vertical asymptotes are x = -1, x = 4

Answer 2

Explanation:

f(x) = 0

Explanation:

The denominator has a higher degree than the numerator, so the horizontal asymptote is f(x) = 0.