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Dandelin
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Missing Sections of Graph with Steep Slopes on HP Prime

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I saw an old post somewhere on the Internet where a user was having difficulty seeing the graph of y=x^4(x-2)(x-6) using a "Decimal" view window and the "Adaptive" method in the Function app. The graph failed to show the branch of the graph with the x-intercept of (6, 0). The reply at the time was to either use a different window or switch to the Advanced Graphing app. I do not care for either of these options since far less-expensive calculators do not have this issue.

 

With a little experimenting, I found that the calculator will graph curves where the absolute value of the slope (derivative) is less than approximately 375 * (Ymaximum - Yminimum) / (Xmaximim - Xminimum) where the maxima and minima refer to values specified in the Plot Setup. When the curve is steeper than this quantity, the curve has holes and gaps until this value exceeds approximately 1500 *(Ymaximum - Yminimum) / (Xmaximim - Xminimum). At this upper value, the curve is usually not graphed at all. These expressions are based on studying graphs of the polynomial given above, y=1/x and y=e^x for various Plot Setup values.

 

I realize with the touchscreen option on the HP Prime for resizing the graphing window, the calculator developers have to be a little more sophisticated in how they have the calculator determine what to graph. The current "Adaptive" method is too risky for me to use unless I already know quite a bit about the graph. And switching over to Advanced Graphing is too slow. Is HP working on another option or is there perhaps a setting on the calculator that I am not using to its full potential?

 

I have only used the calculator for a few days, but others who have used the calculator for much longer are also stumped. Thanks for whatever info. you can send our way.

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Tim_Wessman
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It is being looked at. I cannot say when/if there will be any change however due to HP policy regarding "future looking statements".

 

However, graphing is one of those things that is "deceptively simple" in that it appears to be quite easy but is actually infinitely difficult. It has actually been mathematically proven that you *cannot* create an algorithm to be completely accurate for even simple algebra. All graphing engines thus turn into either a very basic method that falls apart quickly for anything other then the cetain cases it is good at, to a series of different behaviors for different types of  problems in an attempt to adjust for different types of situations.

 

The general way graphing was done in the past was "move one pixel, evaluate, and connect the dots". This works for some simple things, but falls apart rather quickly. Most calculators except the Prime on the market at the moment are using some "smoothing" techniques to kind of hide the types of problems this method can generate and generally work well for simple cases. While that does hide things, the problem is that it hides things. 🙂 In more complicated cases, it actually makes things quite worse.

 

In this simple case, most systems actually get the "correct" result because they always assume that a large jump in values should have a line drawn to connect them. This will directly result in other cases where it draws a vertical line at an asymtote that shouldn't be there. This is why things like TAN(X) will very often get vertical asymtotes where there shouldn't be any. To try and avoid this, you need some code to do special analysis in those cases to start trying to filter out the false positives. It looks like in this case, it is incorrectly filtering out and eliminating the line here.

 

For another fun thing, try the simple "sin(e^x)" example on all your systems. You'll get some pretty crazy things here and strange patterns where there shouldn't be any. The "adapative" on prime will be closer, but only the advanced grapher with its interval graphing gets it correct.

 

So in short, yes - you've brought this to our attention. In long, graphing is actually much more complicated then one might expect. 🙂

TW

Although I work for the HP calculator group as a head developer of the HP Prime, the views and opinions I post here are my own.

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Dandelin
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I am surprised that, after two days, no one has responded about the HP Prime producing inaccurate graphs with the Function app. Is it because:

(a) It is a known issue by the more experienced users, so few users use that app?

(b) There are ways to work around it, but it is too complicated to explain in this forum?

(c) Users were not aware of the problem?

(d) ?

 

If the answer is (c), let me explain the problem again. I graphed the polynomial F1(x)=x^4*(x-2)*(x-6) using View Decimal under View and Adaptive Method under Plot Setup. The graph showed the curve intersecting the x-axis at x=0 and x=2 as expected; however, no curve appeared anywhere in the vicinity of x=6 where the curve should intersect the x-axis again. An entire branch of the curve is missing from the plot window!

 

I was just introduced to the HP Prime this week. I think it is a wonderful calculator in the making, but this graphing issue is very troubling to me. (My TI calculators graph this correctly,)  Am I missing something? Thanks!

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andy11
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@Dandelin wrote:

I am surprised that, after two days, no one has responded about the HP Prime producing inaccurate graphs with the Function app. Is it because:

(a) It is a known issue by the more experienced users, so few users use that app?

(b) There are ways to work around it, but it is too complicated to explain in this forum?

(c) Users were not aware of the problem?

(d) ?

 


The answer is (d): Your post are muuuch toooo looong and you have not provided any picture of the graphs

Although your English is very good and problem is carefully described many people here are not native English speakers and the more you write the more time is needed to understand your problem and correctly answer.

Pls add some picture with the graphs which make problem and give the settings you used to make the graphs

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Dandelin
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The Function app on the HP Prime sometimes creates graphs that are incomplete.

 

Example: y=x^4*(x-2)*(x-6)

 

Here is the graph created using default settings (View Decimal and Plot Setup Adaptive Method):

 Original.jpg

 

Stretching the vertical axis (-100 < y < 100) creates the following graph:

 Modified.jpg

 

Even though both graphs were created using the Function app, only the second graph shows what I would expect. An entire branch of the polynomial function is missing with the default settings. I find this very scary. And remember, this is a fairly simple, though steep, function. 

 

There is a lot I like about this calculator, so I hope HP is addressing this issue.  In the mean time, any suggestions other than using the Advanced Graphing app or a competitor's color graphing calculator instead?

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Maké
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Hi!, @Dandelin:

 

 

Kind Regards !.
Have a nice day !.
@Maké (Technical Advisor Premium - HP Program Top Contributor).
Provost in HP Spanish Public Forum ... https://h30467.www3.hp.com/
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Dandelin
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Thank you Andy and Make' for your suggestions. Once the images of my two graphs are approved for display, I will resume the conversation.

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Dandelin
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Thank you Maké for the Wolfram Alpha plots of y=x^4*(x-2)*(x-6). Those plots also show the portion of the polynomial curve that the Function app on the HP Prime fails to graph (using the default viewing window).

 

Being accustomed to using a calculator that graphs ALL of a function's curve that resides in ANY specified viewing window,  I find the performance of the Function app mind-boggling. I hope I am missing something--after all, what value is a graphing  feature if it cannot be trusted to create accurate graphs? If anyone sees something that I don't, please let me know. Thank you very, very much!

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andy11
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@Dandelin wrote:

I saw an old post somewhere on the Internet where a user was having difficulty seeing the graph of y=x^4(x-2)(x-6) using a "Decimal" view window and the "Adaptive" method in the Function app. The graph failed to show the branch of the graph with the x-intercept of (6, 0). The reply at the time was to either use a different window or switch to the Advanced Graphing app. I do not care for either of these options since far less-expensive calculators do not have this issue.

 


Looking at the graphs you and Make provided everything seems to be normal IMO. No graphing software I know can guess what parts of the graph the user would like to see. If default values of the graphing app do not cover the field you are interested in you can change them.

As for the other user mentioned above complaining on the internet about problems while seeing his graphs and replies to his post I would say that Internet is full of opinions of inexperienced users complaining about everything what behaves the other way they expected.

On the other hand the Prime with touch screen should have a feature of changing scale and moving graph on the screen using the touch panel.

BTW. which far less expensive calculators do not have the "issue" you are complaining about?

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Dandelin
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Andy,

Thanks again for your time, patience, and help in providing clarity to this problem. I will address each of your points which I have typed in bold.

 

Looking at the graphs you and Make provided, everything seems to be normal IMO. No graphing software I know can guess what parts of the graph the user would like to see.

 

Here are the graphs as produced on the HP Prime using the Funcion app. Note that the domain is the same for both plots--the minimum x-value is -16 and the maximum x-value is 15.9 for both. The only difference in the viewing windows is in the range. What bothers me (to no end?) is that only the second graph correctly shows the function passing through the point (6,0). The first graph, at least to me, indicates that the function has no zeros between 2 and 15.9. I am not asking the calculator to "guess what parts of the graph the user would like to see." It knows I asked to see everything on the interval -16<x<15.9, but it failed to do that in the first graph.

 

 

Original.jpgModified.jpg

 

If default values of the graphing app do not cover the field you are interested in you can change them.

The default values in the above case DO cover the field of interest. I want to see all of the x-intercepts in the interval -16<x<15.9. Both viewing windows have exactly that domain, but again, only the second graph actually shows the entire curve that should be visible with the given viewing window. 

 

As for the other user mentioned above complaining on the internet about problems while seeing his graphs and replies to his post I would say that Internet is full of opinions of inexperienced users complaining about everything what behaves the other way they expected.

I have not been able to find the original posting of this issue on the Internet, so I cannot speak for that person. I will also admit that my experience with HP calculators is quite limited. I have been using mostly Texas Instrument calculators the past 20 years as a high school precalculus and calculus teacher, so my expectations may be quite different in some areas. 

 

On the other hand the Prime with touch screen should have a feature of changing scale and moving graph on the screen using the touch panel.

The fact that the HP Prime uses a touch-screen enabled viewing window does, I'm sure, bring in some interesting engineering challenges. All I am saying here is that the current logic used for the Adaptive Method in the Function app seems to need some fine tuning in order to make it more trust worthy.

 

BTW. which far less expensive calculators do not have the "issue" you are complaining about?

I have yet to find a TI calculator that has this issue. The TI-83 Plus, TI-84 Plus, TI-84 Plus Silver Edition, TI-84 Plus CE, and the TI-nSpire CX are all calculators that I have tested using their standard windows. All of theses calculators show the x-intercept at x=6.

 

Again, thank you for your help and hope we can resolve this soon. 

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andy11
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Dandelin, you are right.

I'm sorry but I overlooked somehow the key point of your mails (I was practising fast reding for years what is OK but  sometimes can have a weak point - one can overlook something important sometimes. I overlooked the vertical on the right in the 2nd plot)

Part of the graph is really missing in the 1st plot. I'm sorry but I was to lazy to check this on my hp50g and TI-nspire. Later checking really gave correct plot on TI nspire and even on old Sharp EL-9600.

So, I'm afraid the ball is on HP developers' side now.

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