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The graph you provided is a parabola that opens upwards, which suggests that the function shown is quadratic, likely of the form \( f(x) = ax^2 + bx + c \). To determine where the function is **increasing**, we need to focus on the slope of the curve.

### Key observations:
- The function decreases before reaching its lowest point (vertex), and then increases afterward.
- The vertex of this parabola appears to be at the point \( x = 1 \).
- To the left of \( x = 1 \) (i.e., when \( x < 1 \)), the function is decreasing.
- To the right of \( x = 1 \) (i.e., when \( x > 1 \)), the function is increasing.

### Domain where the function is increasing:
The function starts increasing after the vertex, so the domain where the function is increasing is \( x > 1 \). In interval notation, this is:

\[
(1, \infty)
\]

Would you like more details on how to determine increasing/decreasing intervals using calculus or the derivative of a function?

### Related Questions:
1. How can you find the vertex of any quadratic function using its equation?
2. What is the first derivative test and how can it help determine increasing/decreasing intervals?
3. What is the general form of a quadratic function, and how does the sign of the leading coefficient affect the direction of the parabola?
4. How can you determine if a function is increasing or decreasing without graphing it?
5. How does the second derivative relate to the concavity of the function's graph?

**Tip:** In any quadratic function, the vertex divides the function into increasing and decreasing intervals.

Determine the domain on which the following function is increasing.

Learn how to determine the domain on which a quadratic function is increasing. This involves understanding the vertex of a parabola and applying the first derivative test. Suitable for high school students in Grades 9-12.

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