Find Where f(x) < 0: Analyzing Function Values Between x = 1 and x = 7

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 the problem of determining where f(x)<0 f(x) < 0 :

  • Step 1: Identify the x-intercepts of the graph, which are x=1 x = 1 and x=7 x = 7 .
  • Step 2: Examine the section of the graph between these intercepts. Since the graph dips below the x-axis between these values, f(x)<0 f(x) < 0 in that interval.

Therefore, the function is negative between the roots, i.e., 1<x<7 1 < x < 7 .

Thus, the solution to the problem is: 1<x<7 1 < x < 7 .

Answer

1 < x < 7