find the horizontal and vertical asymptotes for the function.\nf(x) = \\frac{x + 4}{(x + 2)(x…

find the horizontal and vertical asymptotes for the function.\nf(x) = \\frac{x + 4}{(x + 2)(x - 3)}\nvertical asymptotes: x = -2, x = ?\nhorizontal asymptote: y =

find the horizontal and vertical asymptotes for the function.\nf(x) = \\frac{x + 4}{(x + 2)(x - 3)}\nvertical asymptotes: x = -2, x = ?\nhorizontal asymptote: y =

Answer

Explanation:

Step1: Find vertical asymptotes

Set the denominator equal to 0. Given the denominator is ((x + 2)(x - 3)), then ((x + 2)(x - 3)=0). Using the zero - product property, (x+2 = 0) gives (x=-2) and (x - 3=0) gives (x = 3).

Step2: Find horizontal asymptote

The degree of the numerator (n = 1) (since the highest power of (x) in the numerator (x+4) is 1) and the degree of the denominator (m=2) (since ((x + 2)(x - 3)=x^{2}-x - 6)). When (n<m), the horizontal asymptote is (y = 0).

Answer:

Vertical asymptotes: (x=-2,x = 3) Horizontal asymptote: (y = 0)