Question

What are the limitations of determining a function’s average rate of change by examining the function’s graph?

Answer 1

The limitations of determining a function's average rate of change by examining the function's graph include incomplete information, the need for tangent lines, and limited interval-specific data.

Step-by-step explanation:

When determining a function's average rate of change by examining the function's graph, there are several limitations to consider.

1. The graph may not provide enough information about the function's behavior between plotted points, leading to an inaccurate estimation of the average rate of change.
2. A curved graph may require the use of tangent lines to calculate the instantaneous rate of change, which may not accurately represent the average rate of change.
3. The graph may not show the function's behavior in different intervals or at certain points, making it difficult to determine the average rate of change for specific intervals or points.

These limitations highlight the importance of understanding the limitations of graph analysis and considering alternative methods, such as calculus, to accurately calculate the average rate of change of a function.

Answer 2

When using the graph of a function, it is possible to find the average rate of change over only those intervals whose endpoints are visible on the graph. you can also get only approximate values of f(x) from the graph.