find the horizontal and vertical asymptotes for the function.\nf(x) = \\frac{8x^{2}-48x + 72}{x^{2}-6x…

find the horizontal and vertical asymptotes for the function.\nf(x) = \\frac{8x^{2}-48x + 72}{x^{2}-6x - 7}\nvertical asymptotes: x = -1, x = ?\nhorizontal asymptote: y =

find the horizontal and vertical asymptotes for the function.\nf(x) = \\frac{8x^{2}-48x + 72}{x^{2}-6x - 7}\nvertical asymptotes: x = -1, x = ?\nhorizontal asymptote: y =

Answer

Explanation:

Step1: Find vertical asymptotes

Set the denominator equal to 0. Solve $x^{2}-6x - 7=0$. Factor the quadratic: $(x + 1)(x - 7)=0$. So $x=-1$ or $x = 7$.

Step2: Find horizontal asymptote

Since the degree of the numerator and denominator are the same (both degree 2), divide the leading - coefficients. The leading coefficient of the numerator is 8 and of the denominator is 1. So $y=\frac{8}{1}=8$.

Answer:

Vertical asymptotes: $x=-1,x = 7$ Horizontal asymptote: $y = 8$