Solve f(x) < 0: Finding Points Where Function is Negative

Find all values of $x$

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

To solve the problem of finding where $f(x) < 0$, we need to analyze the graph of the function:

• Examine the graph to identify the intervals where it lies below the $x$-axis.
• The graph crosses the $x$-axis at two key points, $x = 8$ and the line extends indefinitely.
• Thus, the function $f(x)$ is negative when it moves below the $x$-axis on either side of $x=8$.

From this graphical analysis, $f(x)$ is negative for:

• The range $x < 8$: The part of the graph to the left of $x = 8$ is under the $x$-axis.
• The range $x > 8$: The part of the graph to the right of $x = 8$ is also under the $x$-axis.

Therefore, the solution to the problem is that $f(x) < 0$ for $x < 8$ or $x > 8$.

This matches the answer choice $x < 8$ or $8 < x$.