determine the domain on which the following graph of f(x) is negative.

Explanation:

Step1: Identify where the function is negative.

The function $f(x)$ is negative where its graph lies below the x-axis ($y < 0$).

Step2: Find the x-intercepts.

Observe the graph to find the points where it crosses the x-axis. The x-intercepts are at $x = -4$ and $x = 0$.

Step3: Determine the intervals for negative values.

The graph is below the x-axis for x-values less than $-4$ and for x-values greater than $0$.

Step4: Express the domain in interval notation.

The domain where $f(x)$ is negative consists of two intervals: $(-\infty, -4)$ and $(0, \infty)$. The union represents the complete domain. $$(-\infty, -4) \cup (0, \infty)$$

Answer:

The domain on which the graph of $f(x)$ is negative is $(-\infty, -4) \cup (0, \infty)$.