Find Where f(x) < 0: Analyzing Function with Critical Points at -10, -6, and -2

Question

Find all values of x x

where f\left(x\right) < 0 .

XXXYYY-6-6-6-10-10-10-2-2-2

Step-by-Step Solution

To solve the problem of finding all x x values where f(x)<0 f(x) < 0 , we analyze the graph provided:

The graph of the function f(x) f(x) shows it is below the x-axis in the interval from x=10 x = -10 to x=2 x = -2 . Between these points, f(x) f(x) is negative because the complete span of the graph resides beneath the x-axis between these points.

Steps to validate this are:

  • Recognize the x-intercepts, which occur at x=10 x = -10 and x=2 x = -2 , where the curve crosses the x-axis.
  • The graph stays below the x-axis between these intercepts, indicating the function is negative.

Thus, the correct interval where f(x)<0 f(x) < 0 is 10<x<2-10 < x < -2.

Therefore, the solution to the problem is 10<x<2-10 < x < -2.

Answer

-10 < x < -2