To determine where $f(x)$ is decreasing, we need to look at the slope of the function, represented by its derivative $f'(x)$. A function is decreasing in regions where $f'(x) < 0$.

From the graph:

1. Identify intervals where the slope of $f(x)$ is negative.
2. Visually inspect where the curve moves downward as $x$ increases.

Based on the image provided, it appears that:

• $f(x)$ is decreasing in the interval $( -\infty, -1)$, where the function descends as $x$ progresses from left to right.
• $f(x)$ starts to increase again after $x = -1$.

So, the interval where $f(x)$ is decreasing is approximately: $(-\infty, -1)$

Would you like further details or have any other questions about this?

Here are five related questions you might find useful:

1. How do you determine intervals of increase for $f(x)$?
2. How can the derivative test be used to confirm intervals of increase or decrease?
3. What happens to $f(x)$ at critical points where $f'(x) = 0$?
4. How do concavity and inflection points affect the graph of $f(x)$?
5. What does it mean if $f(x)$ is constant on an interval?

Tip: When analyzing a function graph, look for the intervals where it slopes downwards to identify where it’s decreasing.