To determine the open intervals where a function is increasing, you need to analyze the graph of the function. An increasing function is characterized by slopes that rise as you move from left to right. This means that for any two points within the interval, the function’s value at the higher x-value will be greater than the value at the lower x-value.
Follow these steps to identify increasing intervals:
- Look for parts of the graph where the curve is sloping upwards as you move from left to right.
- Note the x-values at which these increasing segments start and end. These x-values will help you define the open intervals.
- Write the intervals using parentheses to signify that the endpoints are not included. For example, if a function increases from x = a to x = b, you would denote it as (a, b).
In summary, analyze the graph and list down the intervals where the function consistently rises. This will give you the open intervals where the function is increasing.