Question

For each of the following rational functions, write an equation for every vertical. horizontal and/or slant asymptote. Only fill the boxes that apply, some boxes may remain empty! h(x) =+3x+2 Vertical Horizontal Slant

Answer 1

solution. Explanation: first, you must make sure to understand the situations where the different types of asymptotes appear. vertical asymptotes; - All sational expressions will have a vertical asymptote. put, a vertical asymptote occurs when the denominator is equal to O. Horizontal Asymptotes: - Horizontal asymptotes depend on the maxinum degrees of the numerator and of the denominator, i If the degree of the denominator is higher than that of the numerator, there will be a horizontal asymptote at yao. ii) If the degree of the denominator is equal ! to the degree of the numerator, there will be a horizontal asymptote at the ratio between the coefficients of the highest degree of the function. obliguel slant asymptotes: when the degree of denominator is lower than that of the numerator. the answer There will be an oblique asymptote at to the division of the denominator and the numerator.

Now, w for hele 2 vertical asymptotes: Horizontal asymptote: since, degree of Numerator (degree of denominator ol1 So, there will be a horizontal asymptote at jyo) slant asymptote. No For has to x-2 vertical asymptotes : n-2 0 Horizontal asympto fes : 1 since, degree of denominator a degree of numerator 1 =1 So, there will be a horizontal asymptote at yol stant asymptote; - No

for, hou n²+ 3n+2 x+3 vertical asymptotes & nt30 horizontal asymptote & since, the degree of denominator (degree of Num! There is no horizontal asymptote, there is a slant asymptote. slant asymptote :- +3) % +3/1+2 ( wf you 2 so slant asymptote at: Ty=n) Hence, x+6 holz - +32 +2 hanya 1-2 91-2 Thn) = ? x+3 how - z at x-o at y=0 hem, - at x=-3 vertical Horizontal hoes - hitta at x=2 at y = 1 slant line: y=x