Question

pick the graph of the following function.

(f(x) = (x - 2)(x - 3)(x - 4))

Explanation:

Step1: Identify the x-intercepts

$$x = 2, \quad x = 3, \quad x = 4$$

Step2: Determine the end behavior

$$\lim_{x \to \infty} f(x) = \infty, \quad \lim_{x \to -\infty} f(x) = -\infty$$

Step3: Match with the correct graph

The second graph crosses the x-axis at \(x = 2\), \(3\), and \(4\).

Answer:

The second graph (top row, middle graph).