question 2 of 10\nat which values of x does the function f(x) have a vertical asymptote? check all that…

question 2 of 10\nat which values of x does the function f(x) have a vertical asymptote? check all that apply.\nf(x) = \\frac{1}{x(x + 6)(x - 1)}\na. 0\nb. 6\nc. 1\nd. -1\ne. -6

question 2 of 10\nat which values of x does the function f(x) have a vertical asymptote? check all that apply.\nf(x) = \\frac{1}{x(x + 6)(x - 1)}\na. 0\nb. 6\nc. 1\nd. -1\ne. -6

Answer

Explanation:

Step1: Recall vertical - asymptote condition

A rational function $F(x)=\frac{g(x)}{h(x)}$ has vertical asymptotes at the values of $x$ for which $h(x) = 0$ and $g(x)\neq0$. Here, $g(x)=1$ and $h(x)=x(x + 6)(x - 1)$.

Step2: Set the denominator equal to zero

Set $x(x + 6)(x - 1)=0$. Using the zero - product property, if $abc = 0$, then $a = 0$ or $b = 0$ or $c = 0$. So, $x=0$ or $x+6 = 0$ or $x - 1=0$.

Step3: Solve for $x$

If $x+6 = 0$, then $x=-6$. If $x - 1=0$, then $x = 1$.

Answer:

A. 0, C. 1, E. -6