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

To determine the values of $x$ at which the function $f(x) > 0$, we analyze the graphically provided quadratic function. The function $f(x)$ is represented as a parabola in the given diagram. We find the points where the parabola intersects the x-axis, marking critical points for determining sign changes in the function.

Upon examining the graph, we identify the x-intercepts at $x = 1$ and $x = 7$. The function changes sign around these x-intercepts as follows:

• For $x < 1$, the graph is above the x-axis, implying $f(x) > 0$.
• For $1 < x < 7$, the graph is below the x-axis, implying $f(x) < 0$.
• For $x > 7$, the graph is again above the x-axis, implying $f(x) > 0$.

Consequently, the solutions where $f(x) > 0$ are at $x < 1$ and $x > 7$. Comparing these results with the given answer options, option 3, which is $x > 7$ or $x < 1$, corresponds precisely to our solution.

Therefore, the correct solution to the problem is $x > 7$ or $x < 1$.