Question

determine the domain on which the following graph of f(x) is negative.

Explanation:

Step1: Identify x-intercepts

The graph intersects the x-axis at \( x = 3 \) and \( x = 7 \).

Step2: Analyze where \( f(x) < 0 \)

A function is negative when its graph is below the x - axis. From the graph, we can see that the graph of \( f(x) \) is below the x - axis when \( x < 3 \) or \( x > 7 \). We use open intervals because at \( x = 3 \) and \( x = 7 \), \( f(x)=0 \) (not negative).

Answer:

\( (-\infty, 3)\cup(7, \infty) \)