https://file.aiquickdraw.com/mathbot/file/172549609585251ubznif.jpg

The image shows a graph of a function, and the task is to determine the domain on which the function is **increasing**.

From the graph, we observe that:

- The function decreases first as it moves downwards, reaches a minimum point, and then starts increasing.
- The minimum point appears to be located around \( x = 1 \) (based on the graph).
- After this point, the graph starts increasing as \( x \) moves to the right.

Thus, the function is increasing for values of \( x > 1 \).

### Answer:
The domain on which the function is increasing is \( (1, \infty) \).

Would you like more details or have any other questions?

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Here are 5 related questions you might want to explore:

1. How do you find intervals where a function is increasing or decreasing using its derivative?
2. What is the formal definition of an increasing function?
3. How can you find critical points of a function algebraically?
4. What does it mean for a function to be decreasing, and how do you identify that interval?
5. How can you apply the first derivative test to determine intervals of increase or decrease?

**Tip**: To determine where a function is increasing or decreasing algebraically, take its derivative. The function is increasing where the derivative is positive and decreasing where the derivative is negative.

Determine the domain on which the following function is increasing.

Analyze the graph of a function to determine the domain on which it is increasing. This problem is ideal for students in Grades 10-12, focusing on key concepts in calculus such as derivatives and intervals of increase.

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