quiz 2 lt2\nfill in the blanks\n$f(x)=\\frac{5}{x + 6}-6$\nvertical asymptote: $x =$\nhorizontal asymptote…

Answer:

Vertical asymptote: (x = -6) Horizontal asymptote: (y = -6) (x)-intercept: (x = -\frac{41}{6}) (y)-intercept: (y = -\frac{31}{6})

Explanation:

Step1: Find vertical asymptote

Set denominator (x + 6=0), so (x=-6).

Step2: Find horizontal asymptote

For (y=\frac{5}{x + 6}-6), as (x\to\pm\infty), (\frac{5}{x + 6}\to0), so (y=-6).

Step3: Find (x)-intercept

Set (y = 0), (\frac{5}{x + 6}-6=0), (\frac{5}{x + 6}=6), (6(x + 6)=5), (6x+36 = 5), (6x=-31), (x=-\frac{31}{6}).

Step4: Find (y)-intercept

Set (x = 0), (y=\frac{5}{0 + 6}-6=\frac{5}{6}-6=\frac{5 - 36}{6}=-\frac{31}{6}).