Question

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

Explanation:

Step1: Identify x-intercepts

The graph intersects the x - axis at \(x = 1\) and \(x=9\).

Step2: Analyze the sign of \(f(x)\)

For a parabola opening upwards (since the coefficient of \(x^{2}\) is positive, as the parabola opens upwards), the function \(f(x)\) is positive when \(x\) is less than the smaller root or greater than the larger root. So, \(f(x)>0\) when \(x < 1\) or \(x>9\).

Answer:

The domain on which \(f(x)\) is positive is \(x\in(-\infty, 1)\cup(9,+\infty)\)