Answer:
B. vertical asymptote: x = 1
horizontal asymptote: y = 0
Step-by-step explanation:
1) Vertical asymptotes of a function are determined by what input of x makes the denominator equal 0. So, let's set the denominator, [tex]x^3-1[/tex], equal to 0 and solve for x:
[tex]x^3-1= 0\\x^3 = 1\\\sqrt[3]{x^3} = \sqrt[3]{1} \\x = 1[/tex]
Thus, the vertical asymptote is x = 1.
2) If the degree of the polynomial in the denominator is greater than the one on the top, the horizontal asymptote is automatically y = 0. Thus, the horizontal asymptote is y = 0.
Answer:
B. x=1, y=0
Step-by-step explanation:
Vertical asymptote: denominator approximate 0
(x²+x-6)/(x³-1) ---> ±∞ as x ---> 1
x³-1 = 0
x³ = 1
x = ∛1 = 1
Horizontal asymptote: If the degree of the numerator is less than the degree of the denominator, then the horizontal asymptote is always the x axis, i.e. the line y = 0
degree of the numerator: 2
degree of the denominator: 3
2<3
Horizontal asymptote: y = 0