Questions: Question 13 Select the choice that is a graph of the function f(x) = 3 (x-2) / ((x+2)(x-3))

Solution Steps

The given function is \( f(x) = \frac{3(x-2)}{(x+2)(x-3)} \) The function has vertical asymptotes at \(x = -2\) and \(x = 3\), and a horizontal asymptote at \(y = 0\). The x-intercept is at \(x = 2\).

The first graph has vertical asymptotes at \(x=-2\) and \(x=3\), and appears to have an x-intercept at \(x=2\).

The second graph has vertical asymptotes at \(x=2\) and \(x=3\).

The third graph has vertical asymptotes at \(x=-2\) and \(x=3\), and an x-intercept at around \(x=-0.5\).

The fourth graph has vertical asymptotes at \(x=-2\) and \(x=3\), and appears to have an x-intercept close to \(x=0\).

Final Answer The first graph.