The function f(x) can have vertical asymptotes and horizontal asymptotes.
To find the vertical asymptotes, we need to determine the values of x for which the denominator (x^2 + 6x + 5) becomes zero.
The denominator factors as (x + 5)(x + 1), so it equals zero when x = -5 or x = -1. Therefore, we have two vertical asymptotes: x = -5 and x = -1.
To find the horizontal asymptotes, we consider the behavior of the function as x approaches positive or negative infinity.
As x approaches positive or negative infinity, the leading terms dominate the function. The leading terms in this case are x/x^2 = 1/x, which approaches 0 as x approaches infinity or negative infinity.
Therefore, we have one horizontal asymptote: y = 0.
Therefore, the correct answers are:
A. y = 0
B. x = -5
For the Function f(x)=x+1/x^2+6x+5 find the equation of any asymptotes. Select the two correct answers.
A. y=0
B. x=-5
C. y=-5
D. y=-1
E. x=-1
1 answer