Final answer:
To determine increasing and decreasing intervals on a graph, observe the slope of the graph as you move from left to right, identify turning points, and note the x-values that correspond to the intervals where the graph's slope is positive (increasing) and negative (decreasing). Use precise tools and scale the axes for clarity.
Step-by-step explanation:
To find the increasing and decreasing intervals on a graph, you need to look at the slope of the graph as it moves from left to right.
An increasing interval is where the graph is going upward as you move to the right; the function's values are getting larger, which means that the slope is positive. A decreasing interval is where the graph is going downward as you move to the right; the function's values are getting smaller, indicating a negative slope. Here are steps to help in identifying these intervals:
- Observe the graph's overall trend from left to right.
- Identify the points where the graph changes direction; these are called turning points or extrema (maximums and minimums).
- The graph is increasing on intervals between the x-values of these turning points where the function is moving upwards.
- The graph is decreasing on intervals between the x-values of the turning points where the function is moving downwards.
- Label these intervals on the graph or list them, specifying the x-values that bound each increasing or decreasing section.
Remember to use accurate tools like a ruler and pencil if you are constructing or making adjustments to a graph. Also, make sure to properly scale the axes to get a clear view of the function's behavior.