some questions about graphing equations and expressions ??

[bimbo36]

i have few more dumb questions about some basic stuffs ...

 

is it always possible to plot the graphs of algebraic expressions and equations on the graph ???

 

i always had these doubts about variables ...how they were going to look like in a graph ?? about expressions , equations ... and how they are represented in the graph ...

 

are they only going to look like simply points on the graph ??? or you can call it a region ? or something like that ???

 

 

i have been trying to stare into books at free times... trying to fill the missing parts ... its a bit exhaustive .. sometimes i want to look into the books ... then i get double exhausted after staring into the books for a long time ...

 

is this something nice to follow .. ?? i am also trying to understand the concepts of variables involved in an equation.. and how they are going to look like in a graph ....

 

 

this is the only example i could come up with ....

 

 

 

 

 

Edited February 12, 2016 by bimbo36

[bimbo36]

first of all ... thanks for letting me keep the youtube video and picture .. i thought somebody was going to remove it and call it spam ...

 

thanks for not doing that ...

 

i am actually trying to improve my maths from some basics .. which is why my questions looks a bit dumb ...

 

i have few more basic questions to ask ...

 

i am trying to picture an expression or equation with which i can try to do something ...

 

take this one for example ...

 

 

 

i dont know what i could possibly do with a motion of an object in a graph ??

i have been trying to narrow it down to some simple things ...

 

i just cant come up with a proper question to ask ...

 

you can try to find its roots .. differentiate it , integrate it ... ???

 

you can try to see it like a point mass ...polytopes or NURBS ... ??

 

those are a bit of like new terms to me ...

 

please help with some answers ...

as i don't know where i am heading with all these doubts in my mind ...

 

[studiot]

Thanks for the cool vids in post #2. +1

 

Here is a graph question to think about:

 

When you draw a graph will you always get the same graph for the same expression?

Edited February 19, 2016 by studiot

[bimbo36]

its supposed to be same .. yes ...

 

because the numbers you get from the same equation will always be the same ...

 

but how you draw those numbers is a completely different thing ???

[studiot]

its supposed to be same .. yes ...

 

because the numbers you get from the same equation will always be the same ...

 

but how you draw those numbers is a completely different thing ???

 

That would be true if all of mathematics was deterministic.

But folks so often forget that statistics is part of mathematics.

 

Here are three graphs in statistics.

 

You will always get the same graph for the first one since it is simply a historical record of tonnage shipped through the port of Liverpool in the first half of the 20th century.

 

But the next two wil produce many different graphs as they record a random variable.

 

 

I hope this was helpful in your quest, though I am not quire sure exactly what you are looking for.

 

 

 

Edited February 19, 2016 by studiot

[bimbo36]

thanks for the graphs and thanks for taking your valuable time to make a reply ...

 

i think i had some sort of simple physics equations type graphs in my head ... so that it was a bit of fun too to think about it ... mostly equations involving motions of objects at a specific point ... someone also said most of the physics type equations graph are dealt like point mass ...or something like that ...

 

so in the end .. i think its mostly about getting the numbers from the equation and plotting the graph like a point mass ... where the object x is only seen like a point mass ...

 

i haven't come across much graphs that looks like any thing else other than point mass ...

 

maybe i should look for more functions where the functions are capable of plotting regions ...

 

 

 

 

 

but probably the functions are then going to look a bit more complex .. and i might have a hard time understanding the functions themselves ...

 

its like most of the graphs in physics related problems are a bit advanced for me ... i am only thinking about some simple physics equations involving velocity .. acceleration ... etc ... where we could do something about the points in graph which represents something at a given point ...

 

i don't know how a function of a point mass wave looks like on a graph ...?

or what functions are used to represent the more advanced radio waves ... in graph .... ??

 

i am probably messing up my head too much ...

 

 

 

 

i am not sure if most of the physics type equations are deterministic in nature ....

 

anyway thanks ...

 

this probably looks like i have to be looking into a physics book rather than college level maths books ...

 

maybe i should simply stick with the basics ....

[Xerxes]

Well, let's see if I can help.

 

First, do not confuse expressions with equations - equations, as the name suggests always include an "equals", whereas expressions never do.

 

So [math]2x + 1[/math] is an expression, and it cannot be graphed. To see why, suppose a graph is a line in the plane, then you need 2 numbers (say) to specify each point in this plane.

 

But [math]y = x^2[/math] is an equation, and it can be graphed. In mathematics, we try to make life easy by regarding [math]y=x^2[/math] as an identity, and by suggesting there is a function such that [math]f(x)=y=x^2[/math]'

 

This looks like fancy math-speak, right? But all it is saying is that for any object [math]x[/math] there is another object [math]y = x^2[/math]given by our function.

 

One calls the [math]x[/math] in [math]f(x)[/math] as the independent variable, and the [math]y=x^2[/math] as the dependent variable. Which is merely to say that the output of our function depends on its input.

 

So, by convention, the independent variable is plotted on a horizontal axis in a 2-D plane, and the dependent variable is plotted on the vertical axis.

 

As to whether the same function can give rise to more than one graph, the answer may be yes - that is why it is helpful to specify what sort of object the independent variable is (this is called the domain of our function), and equally what sort of object is the dependent variable (this is called the codomain).

 

If these are carefully specified, there need only be 1 graph per function.

 

As an example consider again our function [math]f(x)=y=x^2[/math]. When [math]x[/math] is some whole number, the graph is "ascending", but when [math]x = \frac{1}{a}[/math] for some whole umber [math]a[/math] the graph is "descending". Can you see why?

[bimbo36]

first of all sorry for the delay ... i was bit busy with work ... i could not get a straightforward two hours in front of pc ...

 

thanks for explaining a lot of basic stuffs ...

 

simply depending on the books for answers like these is a bit boring ....

 

as for the last part ... i think its because ...

 

as the bigger x gets ... the bigger x ^2 gets ...

 

and for x=1/a or .... x =1/2 or , x=1/3 ... or x=1/4 ....

 

the value keeps getting smaller ....

 

 

 

 

 

As to whether the same function can give rise to more than one graph, the answer may be yes - that is why it is helpful to specify what sort of object the independent variable is (this is called the domain of our function), and equally what sort of object is the dependent variable (this is called the codomain)

 

this was very helpful ...

 

usually in questions i have seen , they don't mention much about the sort of object .. we are dealing with ?

 

wait .. i guess that's how some physics questions looks like ..?

 

but in some plain maths questions ... things like those are not usually mentioned that way ... its usually simply an x ...

 

maybe in physics type questions .. they are mentioned in a much more broader way .. like .. the point mass object x ...is something like ... a wave or light ? or something like that ???

 

 

Edited February 26, 2016 by bimbo36