Cocalc Lab 03 Functions And Plots Ipynb

In your Calculus course, you will encounter many types of functions. The most beneficial way of understanding how a function behaves is to study its graph. In this lab, we will learn how to use SageMath to create graphs of various functions. SageMath has many built in functions, commands, and constants such as tan⁡(x),expand(… ),π,\tan(x), \textbf{expand}(\dots), \pi,tan(x),expand(…),π, etc. One way to learn more about these is to read the SageMath documentation. The easiest way to do this in the notebook is to use the ?\textbf{?}?

command. This command opens up a new window at the bottom of the screen filled with useful information and examples on how to use the function or command. Use SageMath to bring up the documentation for the plot\textbf{plot}plot command and look through all of the available options you have to customize your graph of a function. We will use this information to plot cos⁡(x)\cos(x)cos(x) as an orange dashed line in the viewing window [−2π,2π]×[−1,1][-2\pi, 2\pi] \times [-1,1][−2π,2π]×[−1,1]. Plot the function f(x)=x−2+1f(x) = \sqrt{x-2} + 1f(x)=x−2​+1 as a green dotted line with the xxx-range being 2≤x≤112 \leq x \leq 112≤x≤11. There was an error while loading.

Please reload this page. In this notebook you will find some examples on working with functions and basic plotting using numpy and pyplot. Documentation can be found here and here. We will frequently be computing with arrays of numbers, so let's see how various elementary computations are defined Try various elementary operations (+,-,*,/). What do the operations x**2 and x**y produce?

And how about x^2? To plot a function fff we first need to evaluate it at a number of points xix_ixi​ and subsequently produce a plot. We can add labels, a legend and change the linestyle of the plots: Matplotlib: Standard Python Visualization Library The first thing we'll do is import two key data analysis modules: pandas and numpy. Let's download and import our primary Canadian Immigration dataset using pandas's read_csv() method.

The file was originally downloaded from 'https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DV0101EN-SkillsNetwork/Data Files/Canada.xlsx', and then prepared in the previous notebook. Set the country name as index - useful for quickly looking up countries using .loc method This material was developed by Aaron Tresham at the University of Hawaii at Hilo and is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. The goal of this lab is to explore the general shape of a function's graph using calculus (i.e., before graphing the function). Topics include increasing/decreasing and concave up/concave down and their relationship with the derivative. Why do we want to do calculus before graphing?

Compare the two graphs below. The first looks like the graph of a quadratic function (parabola), while the second looks like a cubic function. But as you can see from the input, these are both graphs of the same function. If you look at the formula for the function that has been plotted, you will notice it is a cubic polynomial. Based on your precalculus knowledge of polynomials, you should know that the first graph is not complete. However, there are many functions that we don't understand from precalculus alone.

For these functions, calculus can give us the information we need to produce a complete graph. If we can produce a complete graph, then we can see the key features of the function.

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