Solve the Inequality: Find X Where f(x) < 0

Question

Based on the data in the diagram, find for which X values the graph of the function f\left(x\right) < 0

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Step-by-Step Solution

To solve for when f(x) < 0 on the graph, we follow these steps:

  • Step 1: Locate the x-intercepts, where the curve intersects the x-axis. These intercepts are x=2 x = 2 and x=8 x = 8 .

  • Step 2: Analyze the sections determined by these intercepts. The graph is below the x-axis to the left of x=2 x = 2 and to the right of x=8 x = 8 .

By visually inspecting the graph, it is evident that:

  • The function f(x) f(x) is below the x-axis (i.e., negative) for x < 2 and x > 8 .

Therefore, the solution to the problem is that the graph of the function is negative for x > 8 or x < 2 .

Answer

x > 8 or x < 2