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.