question 3 of 10 at which values of x does the function f(x) have a vertical asymptote? check all that…

question 3 of 10 at which values of x does the function f(x) have a vertical asymptote? check all that apply. f(x) = 1 / (x(x + 6)(x - 1)) a. -6 b. -1 c. 0 d. 1 e. 6

question 3 of 10 at which values of x does the function f(x) have a vertical asymptote? check all that apply. f(x) = 1 / (x(x + 6)(x - 1)) a. -6 b. -1 c. 0 d. 1 e. 6

Answer

Explanation:

Step1: Definir asintotas verticales

Las asintotas verticales de una función racional $F(x)=\frac{g(x)}{h(x)}$ se encuentran donde $h(x) = 0$. Aquí, $F(x)=\frac{1}{x(x + 6)(x - 1)}$, entonces $h(x)=x(x + 6)(x - 1)$.

Step2: Resolver $h(x)=0$

Resolvemos la ecuación $x(x + 6)(x - 1)=0$. Usando la propiedad del producto cero: si $abc = 0$, entonces $a = 0$ o $b = 0$ o $c = 0$. Para $x=0$, la ecuación se satisface. Para $x+6 = 0$, entonces $x=-6$. Para $x - 1=0$, entonces $x = 1$.

Answer:

A. -6 C. 0 D. 1