Final answer:
To write intervals of increase and decrease on a graph, look for sections where the slope is positive for increase, and negative for decrease. Zero growth is indicated by a flat line. Intervals are written using brackets or parentheses to include or exclude endpoints, respectively.
Step-by-step explanation:
To write increasing and decreasing intervals on a graph, you need to identify where the function's rate of change is positive (increasing) or negative (decreasing). Consider a function represented by a line on a graph. When the line moves upwards as it progresses from left to right, it indicates the function is increasing. Conversely, a downward trend indicates a decreasing function. For instance, let's say you have a graph that shows growth rate changes over time.
To annotate an interval where growth is increasing linearly, find a section of the graph where the line is straight and has a positive slope. Using the provided example, if you have points (6.4 s, 2000 m) and (0.50 s, 525 m), calculate the slope to confirm it is constant and positive. To annotate a decreasing interval in proportion to the square of the number of cells, look for where the graph curves downwards, which signifies the rate is slowing down as the number of cells grows.
To illustrate an interval with zero growth rate, identify a flat part of the graph where the slope is zero, indicating no change over time. In summarizing the intervals, use brackets or parentheses: a pair of brackets [a, b] indicates the interval includes its endpoints, while a pair of parentheses (a, b) indicates the interval does not include the endpoints. Making annotations directly on the graph or writing them separately with corresponding references can effectively communicate these intervals.