Weird functions

Take a look here

This is extremely weird as both functions are algebraically the same. This kind of thing occurs very frequently but it still leaves me puzzled.

What do you think causes the difference when graphing them?

#Functions #Graphs #Weird

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

In the first place, Sin(xy) is supposed to be a surface, so the green graph sort of looks like the way it's supposed to be (however badly drawn). In theory, both functions are the same, but apparently your graphing calculator has a hangup with the first one. If you use a good math software like Mathematica, there is no difference. Check this out

SinXY SinXY

Michael Mendrin - 6 years, 6 months ago

I dont really understand why it is a surface though. $\sin{(xy)}=0$ has only $2$ variables.

Julian Poon - 6 years, 6 months ago

Oh, right, I missed the memo that it has to equal to $0$ . Well, you can see where this surface is equal to $0$ , so it agrees with the green graph. Let me try something now.

Yeah, I get the same graph as the green one, with both equations you've posted. For whatever reason, your graphing calculator has a hangup with the series expression. Can you give me other examples of this "weird behavior that keeps frequently", and maybe we can see what your calculator is doing?

Michael Mendrin - 6 years, 6 months ago

@Michael Mendrin – Other examples include this

Julian Poon - 6 years, 6 months ago

@Julian Poon – Well, once again, Mathematica handles this correctly, and shows part of this function $y={ x }^{ 6 }$ in both cases. I think your calculator is just not up to this job. I don't think the reason why it shows the line $x=6$ is related to the problems it's having with the first example you gave.

Michael Mendrin - 6 years, 6 months ago

May be the functions are non identical.

Looks at these

f(x) = $ln x^{2}$

g(x) = $2lnx$

Krishna Sharma - 6 years, 6 months ago

Yeah, for a simple case like this the difference can be easily explained. But this one is too complicated and I have no idea what causes this, thats why im posting it.

Nice example by the way :D.

Julian Poon - 6 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$