Question

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

Explanation:

Step1: Understand positive - value condition

A function \(y = f(x)\) is positive when \(y>0\), which means the graph of the function is above the \(x\) - axis.

Step2: Identify intervals from the graph

By observing the graph, we find the \(x\) - values for which the graph is above the \(x\) - axis. Let the \(x\) - intercepts be \(x_1\) and \(x_2\) (where the graph crosses the \(x\) - axis). The function \(f(x)\) is positive for \(x_1

Answer:

The domain on which \(f(x)\) is positive is the open - interval between the two \(x\) - intercepts of the graph (the values of \(x\) for which the graph of \(y = f(x)\) lies above the \(x\) - axis). Without specific numerical values of the \(x\) - intercepts from the graph, we can represent it as \((a,b)\) where \(a\) and \(b\) are the \(x\) - coordinates of the left - hand and right - hand \(x\) - intercepts respectively.