Graphing Functions on a TI-84 Calculator - Lesson 2

Steve Sobek introduces the video's purpose: teaching viewers how to graph various types of functions on a TI-84 graphics calculator. He explains the process of modifying line types and colors if the calculator has color capabilities. The concept of a 'suitable viewing window' is introduced, which is essential for observing specific features of the graph such as x-intercepts, relative maxima and minima, and intersections of multiple functions. The importance of adjusting the viewing window to focus on these features is emphasized, setting the stage for the examples that will follow.

The video continues with an example of graphing a linear function, Y = 2x - 4, on the TI-84 calculator. Sobek demonstrates how to input the function and graph it using the 'y=' button. He explains the standard window settings and how to adjust them using the 'Zoom' feature for a better view of the graph. The concept of a suitable viewing window is further developed by discussing how to change the window to see specific features like x-intercepts. Additionally, he shows how to change the color of the graph and how to deactivate and activate functions for teaching purposes.

Sobek discusses how to adjust the viewing window to better visualize functions, using a second linear function, Y = -x + 21, as an example. He explains that if a function's graph is outside the current viewing window, the window settings need to be manually changed to include the graph. By understanding the function's properties, such as the y-intercept and slope, he guides viewers on how to modify the y-max value to bring the graph into view. This step is crucial for applications where the intersection of two functions is of interest.

The tutorial moves on to graphing a quadratic function, which is a second-degree polynomial. Sobek explains the characteristics of a parabola, including its u-shaped graph, and how to identify whether it opens upwards or downwards by looking at the leading coefficient. He demonstrates how to adjust the y-max value in the viewing window to see the entire parabola, including its vertex and x-intercepts, which is essential for a complete understanding of the function's behavior.

Sobek introduces cubic functions, which are third-degree polynomials, and explains their potential behavior based on the leading coefficient. He shows how to graph a cubic function on the TI-84 calculator and discusses the importance of expanding the viewing window to capture the function's complete graph, including x-intercepts and relative extrema. He also mentions the use of the table feature to help determine the appropriate y-min value for the viewing window.

The video covers the graphing of fourth-degree polynomial functions, also known as Cordic functions. Sobek explains the behavior of these functions for extreme values of x and how they differ from cubic functions. He demonstrates the process of adjusting the viewing window, including changing the y-min and x-max values, to ensure the entire function is visible. The summary also includes a brief mention of using the table feature to find the minimum value of the function.

Sobek discusses the use of the box zoom feature on the TI-84 calculator to focus on specific regions of a graph. He shows how to select a rectangular area to zoom in on, which is particularly useful for examining details of the graph, such as intercepts and asymptotes. The video also summarizes the behavior of odd and even degree polynomial functions, explaining how their graphs behave for extreme values and how to identify the direction of the end behavior based on the leading coefficient.

The video concludes with a brief overview of graphing exponential, logarithmic, and trigonometric functions on the TI-84 calculator. Sobek reminds viewers of the characteristics of these functions, such as the asymptotes for exponential and logarithmic functions and the periodic nature of trigonometric functions. He emphasizes the importance of understanding these functions' behaviors to select suitable viewing windows and provides quick tips for graphing them effectively.

In the final part of the video, Sobek addresses rational functions and the challenges of graphing them, especially on older calculators that may connect points misleadingly. He stresses the importance of understanding asymptotes and the behavior of rational functions to avoid misconceptions. The summary highlights the key points covered in the video, including the use of the TI-84 calculator for graphing various types of functions, modifying graph properties, and the significance of selecting appropriate viewing windows. Sobek also encourages viewers to stay tuned for subsequent videos that will delve into problem-solving using graphing calculators.