Question

how many vertical asymptotes does the graph of this function have?
$f(x)=\frac{3}{x(x - 4)}$
a. 1
b. 0
c. 2
d. 3

Explanation:

Step1: Find the denominator's zeros

Set the denominator \(x(x - 4)=0\).
Using the zero - product property \(ab = 0\Rightarrow a=0\) or \(b = 0\), we get \(x=0\) or \(x - 4=0\) (i.e., \(x = 4\)).

Step2: Check for vertical asymptotes

For a rational function \(F(x)=\frac{f(x)}{g(x)}\), vertical asymptotes occur at the values of \(x\) that make \(g(x)=0\) (provided \(f(x)
eq0\) at those values). Here, \(f(x) = 3
eq0\) when \(x = 0\) or \(x=4\).

Answer:

C. 2