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 \(x=-7\) and \(x = 1\).

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

For a parabola opening downwards (since the coefficient of \(x^{2}\) is negative, as the graph opens downward), the function is negative when \(x < - 7\) or \(x>1\) (because the graph is below the x - axis (where \(y = 0\)) for these intervals).

Answer:

The domain where \(f(x)\) is negative is \(x < - 7\) or \(x>1\) (in interval notation, \((-\infty,-7)\cup(1,\infty)\))