Find an appropriate graphing software viewing window for the given function and use it to displa

Find an appropriate graphing software viewing window for the...

Key Concepts

Graphing Software

Graphing software is a tool that allows you to visually represent mathematical functions by plotting them on a coordinate plane. It is essential for analyzing the behavior of functions, identifying key features like intercepts, turning points, and asymptotic behavior, and ensuring that the graph accurately reflects the overall behavior of the function.

Viewing Window Selection

The viewing window in graphing software defines the range of x- and y-values that are displayed on the screen. Choosing an appropriate viewing window is crucial because it ensures that all important characteristics of the function, such as peaks, valleys, intercepts, and end behavior, are visible. A well-chosen window can reveal the complete picture of the function's behavior, while an inappropriate one might obscure significant features.

Polynomial Functions

Polynomial functions are a class of functions characterized by powers of the variable with non-negative integer exponents. Their graphs are smooth and continuous, and they can exhibit behaviors such as multiple turning points, roots, and symmetry. Understanding the fundamental properties of polynomials, including degree and leading coefficient, helps in predicting end behavior and the overall shape of the graph.

Overall Behavior Analysis

Overall behavior analysis involves studying how a function behaves over its entire domain, including its growth, decay, and any turning points or inflection points. This analysis is important when setting the viewing window for a graph because it ensures that both local and global features, such as extreme values and asymptotic trends, are captured, allowing for a comprehensive understanding of the function's dynamics.

Transcript

00:01 Right, so in this problem we are given a function of x and we're asked to find an appropriate viewing window for its graph.

00:17 So what is appropriate window means? that means it should show one, it should give the overall behavior of the function.

00:30 And we are told that there is more than one correct choice but an incorrect choice would be one that makes us or we can't see important aspects of the function so if there is a curve or a funny yeah funny or an asymptote that should be displayed on its window so anything interesting that's going on let's go up for this function, that's with the end.

01:02 So let's start.

01:06 So i grabbed a couple of, well, i graph the same function in different windows.

01:15 So this is the first one.

01:17 It goes from negative, from negative to five and by the same thing.

01:29 And by the same negative 5 to 5.

01:35 So in these coordinates, the first interval is always going to correspond to the y axis, and the second one will always be the y axis.

01:49 So in this case, we have, it goes down here to negative infinity and up to maybe negative, going to be ready and we have this almost line it goes also from it disappears on the top and it disappears on the bottom so from the from the picture that i have here maybe there's an accent here maybe these connect and same with this maybe it goes down and it goes back up but we just can't see it so first thing we're not going to commit to this one just yet next we're just going to zoom out and see if we can see anything interesting that we're missing out on here.

02:41 So i graph from minus 10 to 10 and the same on the y -axis.

02:49 So again we have this, not that we have this zoom out, there is this curve here, but we are still here.

03:01 We still don't see the endpoints in here.

03:06 So, but these do seem to be getting closer, which might suggest that they are connected.

03:12 On these, it looks like they might be going to negative end.

03:16 Again, to make sure we want to zoom out even more.

03:20 So, let's see.

03:22 Aha.

03:23 So, there is a hump over here, which is curve...