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The question in the image asks:

"In interval notation, provide the interval over which \( g(x) \) is increasing (an increasing interval refers to the interval over which its \( y \)-values become larger as its \( x \)-values become larger)."

To solve this, you will need to know the function \( g(x) \). The increasing interval refers to where the function's derivative is positive, meaning the slope of the graph is positive. Without the explicit function \( g(x) \), I can only guide you on how to find the interval if the function was known.

Here's how to find the interval where a function is increasing:

1. Take the derivative of the function, \( g'(x) \).
2. Set the derivative greater than zero \( g'(x) > 0 \) to find where the slope is positive.
3. Solve for \( x \) to find the intervals where the function is increasing.
4. Express these intervals in interval notation, for example, \( (a, b) \).

If you provide the function \( g(x) \), I can help you with the specific steps.

Do you want more details on how to find these intervals or specific help with derivatives? Here are 5 relevant questions for expansion:

1. Do you need help with finding the derivative of a function?
2. Would you like an example problem of how to find increasing intervals?
3. Do you know if the function \( g(x) \) is quadratic, cubic, or something else?
4. Are you familiar with the first derivative test for increasing and decreasing intervals?
5. Do you need help solving inequalities to find intervals?

**Tip**: Always look for where the derivative of a function switches from positive to negative (or vice versa) to identify increasing or decreasing intervals.

In interval notation, provide the interval over which g(x) is increasing (an increasing interval refers to the interval over which its y-values become larger as its x-values become larger).

Learn how to determine the increasing intervals of a function using its derivative. This involves finding where the function's derivative is positive. Suitable for high school calculus students.

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