![]() To put these on the graph I downloaded the image and then added the circles in an image editing program like Paint. This not only shows the discontinuity, but also indicates that the function is undefined at x = -4. An even better version of this graph would be to include open circles at x = -4. In this case, Desmos gives a more accurate graph since it shows the discontinuity at x = -4. Since the angle being computed is that between two rows, the weights of the outgoing edges will be considered. ![]() Desmos would give the opposite conclusion. begingroup Vineet In my understanding, the definition is the same for undirected and directed graphs the example in the answer is actually an undirected graph, since the adjacency matrix is symmetric, although it might as well have been directed. The WolframAlpha graph would lead you to think the function is continuous. But if you were determining whether the function was continuous at x = -4, the two graphs would lead to different conclusions. This is because x = -4 causes the denominator to be zero. This looks similar to the WolframAlpha version, except that the tow horizontal pieces are not connected. Let’s try graphing this function in Desmos.Īs shown in the video above, the graph of this function looks like this in Desmos. This is problematic since this is not a function…it does not pass the vertical line test at x = -4. These sections are connected by a vertical line at x = -4. The graph consists of a horizontal section at y = -1 and another at y = 1. Press return to give the following result. Putting this in front of (x+4) means the absolute value of the quantity x + 4. The absolute value function in WolframAlpha is “abs”. To graph this function in WolframAlpha, go to the website and type this in the box on the screen.īoth the numerator and denominator need to be in parentheses. These two online graphing tools are both free to use and can produce excellent graphs. Depending on the technology you use, the graph you get may not actually represent the function well. But this is essentially what you get if you plug in the values.Graphing an absolute value function can be a bit deceiving. Maybe I can blow this up, take a quick look at that, take a screen grab and then copy that over. ![]() And so I could I would encourage you to just take a quick look at this. The gamma function along part of the real. Where you just type an ally instead of pi and what I get here and see if we can there we go the Excel spreadsheet, you can see that there is um a pretty pretty nice tight correspondence between the two and the air actually gets smaller, the larger the value gets. In mathematics, the gamma function is one commonly used extension of the factorial function. For each of these values in the table as well. I have gone ahead and just simply plug in values for a pi of X. And then finally complete the following table. There's a function here that more or less traces the number of prime numbers that you can plot on this graph, which is very interesting. Now be here plot pivots and ally of ex from Mexico's one Texaco's 100 together and here's that function right here, you can take a screen grab of that once you type in this phrase in Wolfram alpha and you can see that l ibex is sort of like just above the prime number accounting function, which is very interesting. And the answer for why it's a step function is because there's only interest your values in P of X. You can just, you know, screen grab it and paste it over. It's just simply that um that's what the graph looks like. And so that's why it's always going to step up. And the reason it's a step function is because there aren't like a non intentional number of prime numbers, it's always going to be some intrinsic value. And so this is basically what this function does. Wolfram Alpha will surely survive a long time at least as a math tool. So there should be three numbers at five. How many prime numbers are there before five? Well there's 1, 2, 3. The reason it's a step function is because it counts the number of prime numbers before a certain value. You can just type in this phrase and you get this graph. And so we're gonna look at pi of X from 1 to 20 and Wolfram alpha. So what is paybacks? Paybacks is the prime number counting function.
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