Solve the Inequality: Finding Where f(x) > 0 on the Graph

Find all values of $x$

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

The problem requires us to determine where the function $f(x)$, depicted in the graph, is greater than 0. This interval will be where the graph lies above the x-axis. From the visual representation, the parabola intersects the x-axis at $x = 5$.

Given it is a standard parabola opening upwards or downwards, we need to determine the regions of positivity based on its graph above the x-axis. Usually, a quadratic function, if it opens upwards, has negative values between its roots, provided there's a minimum point. If it opens downwards, the opposite is true.

From the graph, observe that the parabola is indeed below the x-axis at point $x = 5$. The function is positive on both sides away from the point where it intersects (the ends of the parabola ascend back above the x-axis).

To find the solution, notice:

• At $x = 5$, the function equals zero at this point.
• The function is positive on the intervals $x < 5$ and $x > 5$.

Thus, the values of $x$ for which $f(x) > 0$ are on the intervals $(-\infty, 5)$ and $(5, \infty)$.

The function $f(x)$ is positive for $x < 5$ or $x > 5$. Therefore, the correct answer is: $x < 5$ or $x > 5$.