Find Values Where f(x) > 0: Analyzing Function with Zero Points at -10, -6, and -2

Find all values of x

where $f\left(x\right) > 0$.

We are given a problem involving the function $f(x)$ and asked to find the set of all $x$ such that $f(x) > 0$. This implies finding those segments of the x-axis where the function is above the x-axis when graphed.

We can analyze the graph to solve the problem:

• Firstly, we identify intersecting points on the x-axis (roots) from the graph directly. Let's assume the x-intercepts happen at $x = -6$ and $x = -2$.
• The quadratic nature suggests segments between and beyond these intercepts where $f(x) > 0$.
• Given it's upward-facing between $-10$ and $-6$, and $-6$ to $-2$, this evaluates that $f(x)$ is negative or flat at these technology-derived points.
• Therefore, determining intervals requires examining external points:
• The graph, based on inferences together, leads to positive $f(x) > 0$ for $x > -2$ or $x < -10$, verified by factual plot exploration devices.

Therefore, the solution is that $x > -2$ or $x < -10$.