Question

question 2 of 10
how many vertical asymptotes does the graph of this function have?
$f(x)=\frac{2}{(x - 1)(x + 3)(x + 8)}$
a. 0
b. 1
c. 3
d. 2

Explanation:

Step1: Recall the condition for vertical asymptotes

For a rational function \( F(x)=\frac{N(x)}{D(x)} \), vertical asymptotes occur at the values of \( x \) that make \( D(x) = 0 \) (assuming \( N(x)
eq0 \) at those values).

Step2: Find the roots of the denominator

Set \( D(x)=(x - 1)(x + 3)(x + 8)=0 \).
Using the zero - product property \( a\times b\times c = 0\) implies \(a = 0\) or \(b = 0\) or \(c = 0\).
If \(x-1=0\), then \(x = 1\); if \(x + 3=0\), then \(x=-3\); if \(x + 8=0\), then \(x=-8\).
Since the numerator \(N(x) = 2
eq0\) for \(x = 1\), \(x=-3\), and \(x=-8\).

Answer:

C. 3