Limiting The Domain When Graphing

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Limiting The Domain When Graphing

OneLetterShor 24 Jan 2019 17:56

I am in taking Trigonometry right now, and we are working on finding the inverse of functions. To do this, we occasionally have to limit the domain so as to make the function pass the horizontal line test. I can seem to figure out how to correctly do this. For example, I am going to use the function y=x² where x≤0. I have tried typing y=x²(x≤0), but it results in the correct shape left of x=0, but then it has a horizontal line at y=0. I can seem to be able to remove that horizontal line. I understand the math behind the horizontal line. It results from the expression (x≤0) outputting 0 when the function passes the y-axis. Can somebody please show how to write the equation correctly? Thanks!

Re: Limiting The Domain When Graphing

OneLetterShor 24 Jan 2019 17:58

There is probably a better place for these questions, so feel free to shout at me :)

Re: Limiting The Domain When Graphing

Trenly 24 Jan 2019 18:23

The TI-83/84/+ cannot do conditional graphing as far as I know. You could set Ymin to 0 in the Window function, but that just hides that part of the graph.

Re: Limiting The Domain When Graphing

kg583 24 Jan 2019 18:53

The trick to removing the horizontal line is to make the calculator think the left side (or whatever portion) of the graph is imaginary and thus can't be displayed. To remove the left side, for example, multiply the equation by $\sqrt{X}/\sqrt{X}$; this is simply equal to 1, but the calculator thinks it's imaginary for the left side (since the square root of a negative number is imaginary). So, for your graph, type in $X^2(\sqrt{X}/\sqrt{X})$. If you wanted to remove the right side instead, replace the factor by $\sqrt{-X}/\sqrt{-X}$, and in general you can adjust the bounds by changing what's under the square root to make the parts you don't want completely imaginary.

The one downside to this method is that the calculator doesn't like $\sqrt{0}/\sqrt{0}$, so instead of graphing for all X≥0 it is only X>0; the difference is barely noticeable on the graph itself.

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The solution to a complex problem is often a simple answer.

Re: Limiting The Domain When Graphing

lirtosiast 24 Jan 2019 21:39

It's better to use e.g. X²/(X≥0). If X≥0, (X≥0) is 1 and the expression is unchanged, so the point displays. If X<0, (X≥0) is 0 so there is a divide-by-zero error, which is suppressed, and the calculator displays nothing.

Re: Limiting The Domain When Graphing

OneLetterShor 30 Jan 2019 17:44

Thank you for this method. Though it may be longer, it definitely looks better.