Overview
This lecture explains how to adjust graphing calculator windows to better visualize functions that do not fit the standard viewing window, using an example function for estimating a limit.
Standard Viewing Window
- The standard viewing window is set to x: -10 to 10 and y: -10 to 10 on most graphing calculators.
- Not all functions are easily visible or properly represented in the standard viewing window.
Adjusting the Viewing Window
- Use the 'Window' button to change the x and y axis ranges manually.
- For functions with limited domains, adjust x min and x max to focus on relevant regions.
- In the example, the function's domain is from negative infinity to 2 and from 2 to 3, so x max does not need to exceed 3.
- For limits at values like x = -8, extend x min far enough to include that value (e.g., x min = -15).
Using Zoom Features
- Use the 'Zoom' menu and select option 6 for the standard window.
- If the function isn't visible, select option 0 'Zoom Fit' to automatically adjust the y-axis while keeping the chosen x-axis range.
- 'Zoom Fit' sets optimal y min and y max values based on the function in the selected x range.
Example Application
- Enter the function carefully with parentheses around the numerator and denominator.
- Set x min to -15 and x max to 4 as per the function's relevant domain and the value for the limit.
- Use 'Zoom Fit' to let the calculator determine appropriate y values for a clear view of the graph.
Key Terms & Definitions
- Standard Viewing Window — The default graphing range (usually x: -10 to 10, y: -10 to 10).
- Domain — All possible input (x) values for which the function is defined.
- Zoom Fit — A calculator feature that adjusts the y-axis for best fit given a set x-axis range.
Action Items / Next Steps
- Practice adjusting the window and using 'Zoom Fit' on your calculator with different functions.
- Ensure proper use of parentheses when entering functions.