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Based on the graph. The graph is decreasing over the intervals_____. Give your answer in interval notation

Looking at the graph, we can observe that the function \( y = f(x) \) is a decreasing function over certain intervals.

The graph shows a hyperbolic-like curve, and the function appears to be decreasing as you move from left to right. Specifically, it decreases in the interval where \( x > 0 \), starting from \( x = 1 \) onwards. This can be identified because the slope of the graph is negative in that region (i.e., the curve is moving downward).

Thus, the function is decreasing over the interval:

\[
(1, \infty)
\]

Would you like further explanation, or do you have any questions?

Here are 5 related questions to expand on this topic:
1. What is interval notation, and how does it describe increasing or decreasing behavior?
2. How can you determine if a function is increasing or decreasing from its graph?
3. What are the conditions for a function to be decreasing in terms of its derivative?
4. How would you describe the behavior of the function near \( x = 1 \)?
5. What role do asymptotes play in identifying the behavior of functions?

**Tip:** When identifying increasing or decreasing intervals, always observe the slope or direction of the curve. A negative slope indicates decreasing behavior.

Determine the intervals where a function is decreasing based on the graph provided. This problem involves understanding interval notation and recognizing decreasing behavior from the graph. Suitable for students in Grades 9-12.

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