Math help (1 Viewer)

[deswa1]

Re: Math help (Because Carrot made me do this)

^That doesn't go through the origin...

 

[Fawun]

Re: Math help (Because Carrot made me do this)

^That doesn't go through the origin...

Question G.

I don't know. I'm confused.

 

[Sy123]

Re: Math help (Because Carrot made me do this)

That graph cannot go through the origin.
But to sketch this, first find domain and range, the domain is all x less than or equal to 2. The range is y is less than or equal to zero. This is because anything inside the square root is always positive (or zero), so if we do: No matter what is inside f(x), the lowest value we can get is 0, and because the lowest value in that square root is zero, the highest value of 1-sqrt is going to be 1, since 1-0=1.

So we found or domain and range, now we will test big negative values of x, because we need to see where the curve is going (if the domain specifies that negative large numbers arent counted, then test positive large numbers), if we test, say x=-100, we find that the y value is going to be a big negative y value.

Find intercepts, find the end point of the function (the point where the domain and range values 'meet', in this case the end point of the graph will be (1,2), so then we sketch the general shape of it starting from the endpoint, going through respective intercepts

The answer is completely dead wrong

 

[seanieg89]

Re: Math help (Because Carrot made me do this)

I used to do this as well as a last resort - pretty fool-proof at times I reckon.

Graph



on its largest possible domain inside the interval .

 

[Fawun]

Re: Math help (Because Carrot made me do this)

That graph cannot go through the origin.
But to sketch this, first find domain and range, the domain is all x less than or equal to 2. The range is y is less than or equal to zero. This is because anything inside the square root is always positive (or zero), so if we do: No matter what is inside f(x), the lowest value we can get is 0, and because the lowest value in that square root is zero, the highest value of 1-sqrt is going to be 1, since 1-0=1.

So we found or domain and range, now we will test big negative values of x, because we need to see where the curve is going (if the domain specifies that negative large numbers arent counted, then test positive large numbers), if we test, say x=-100, we find that the y value is going to be a big negative y value.

Find intercepts, find the end point of the function (the point where the domain and range values 'meet', in this case the end point of the graph will be (1,2), so then we sketch the general shape of it starting from the endpoint, going through respective intercepts

The answer is completely dead wrong

1. Do you always have to find the domain and range for every question? Like what do I do with the domain and range? does that help me graph it? because if it does, then what's the point of finding the intercepts?

2. When we test those negative numbers do we plot those on the graph as well?
3. How do we know which direction the line goes in? like left, right, down, up? because once I have two points from subbing x=0 and y=0, I draw a curve but I don't know which way to draw it and is two points enough? or would I need to sub in like x=1 and y=1 to find more points?

 

[Shadowdude]

Re: Math help (Because Carrot made me do this)

teaching a graphics based subject on a text based interface... again, not the best way <_<

For your questions:

1. You don't have to, but you have to. It won't be explicit, but to be able to draw the graph you must know domain and range.
2. If the input has an output, then you graph it. If it's error, then it's not defined there. Like if you tried to graph y = 1/x at x = 0, what would you "plot"?
3. That comes through a knowledge of basic graphs. You should know the equation of a line, and thus know if you have two points on the line - you can draw the whole line. If you tried drawing a parabola with two points, you have a very high chance of getting it wrong.


srsly fawun, the best way for you - i think - would be to arrange an in person meeting with someone knowledgeable to actually teach you graphing.

 

[Sy123]

Re: Math help (Because Carrot made me do this)

1. Do you always have to find the domain and range for every question? Like what do I do with the domain and range? does that help me graph it? because if it does, then what's the point of finding the intercepts?

2. When we test those negative numbers do we plot those on the graph as well?
3. How do we know which direction the line goes in? like left, right, down, up? because once I have two points from subbing x=0 and y=0, I draw a curve but I don't know which way to draw it and is two points enough? or would I need to sub in like x=1 and y=1 to find more points?

We dont really need to find domain and range, it just helps immensly, for example if our domain was y> 1, then when we graph it we know that the graph cannot go lower than y=1, likewise, if our range is x<2 for example, we know that x cannot be greater than 2, so we dont go 'past' x=2 when we graph it



In the above picture is an indication of domain and range, for y<1 and x<2, we have our domain and range specified for x<2 it is shaded in green, for y<1 it is shaded in blue, and the section cut off by the grey line is our domain and range, so in that sector the graph will be there.

Testing those large numbers you dont need to plot (though this can help alot too with determining shape), they help with the situation in number 3, in order for us to determine shape of the curve. For example if we put in a large positive value for say:
When we put in x=100, we get the answer as y=-9, so we know that as x goes further and further to infinity, our y value keeps decreasing and decreasing, however the y decreases at a 'slower' rate than x increases, so we demonstrate the curve as such.

Remember its not always negative infinity for square root functions, if negative infinity is outside the domain, test positive, if positive outside domain test negative infinity.

All in all I would not call plotting points a noob way of doing things, in reality the noob way would be to memorise how the curve looks like than rote how to translate the curve (up down left right etc) (im assuming this is what your friends do)

 

[barbernator]

Re: Math help (Because Carrot made me do this)

teaching a graphics based subject on a text based interface... again, not the best way <_<

For your questions:

1. You don't have to, but you have to. It won't be explicit, but to be able to draw the graph you must know domain and range.
2. If the input has an output, then you graph it. If it's error, then it's not defined there. Like if you tried to graph y = 1/x at x = 0, what would you "plot"?
3. That comes through a knowledge of basic graphs. You should know the equation of a line, and thus know if you have two points on the line - you can draw the whole line. If you tried drawing a parabola with two points, you have a very high chance of getting it wrong.

A useful bit of theory. There is only 1 polynomial of degree n that passes through n+1 distinct points. i.e. for a parabola, if you have 3 points, you can find the equation of the parabola, 2 for a line, 4 for a cubic etc.

 

[seanieg89]

Re: Math help (Because Carrot made me do this)

A useful bit of theory. There is only 1 polynomial of degree n that passes through n+1 distinct points. i.e. for a parabola, if you have 3 points, you can find the equation of the parabola, 2 for a line, 4 for a cubic etc.

Provided that no pair of these points have the same x coordinate, but different y coordinates of course.

 

[Sy123]

Re: Math help (Because Carrot made me do this)

A useful bit of theory. There is only 1 polynomial of degree n that passes through n+1 distinct points. i.e. for a parabola, if you have 3 points, you can find the equation of the parabola, 2 for a line, 4 for a cubic etc.

Is this because for example:



So if we have an (n+1) number of points, we have an (n+1) number of y and x pairs, hence we can simultaneously solve for every constant?

 

[seanieg89]

Re: Math help (Because Carrot made me do this)

Is this because for example:



So if we have an (n+1) number of points, we have an (n+1) number of y and x pairs, hence we can simultaneously solve for every constant?

Kind of, but we would technically need to prove that no pair of these equations are redundant or contradictory, which isn't obvious. A more transparent way of proving this is by trying to construct the polynomial explicitly.

EDIT. I strongly recommend you try to find an expression for this polynomial using sum and product notation until it seems like you aren't getting any closer to the solution. At this point, google Lagrange Interpolation.

(But it is much simpler to figure out yourself than the name might suggest.)

 

[twinklegal19]

Re: Math help (Because Carrot made me do this)

srsly fawun, the best way for you - i think - would be to arrange an in person meeting with someone knowledgeable to actually teach you graphing.

this

it's much more efficient

 

[Shadowdude]

Re: Math help (Because Carrot made me do this)

oh, if no one else volunteers - i suppose i can do it

might as well. suggested it, might as well suggest myself

 

[Fawun]

Re: Math help (Because Carrot made me do this)

We dont really need to find domain and range, it just helps immensly, for example if our domain was y> 1, then when we graph it we know that the graph cannot go lower than y=1, likewise, if our range is x<2 for example, we know that x cannot be greater than 2, so we dont go 'past' x=2 when we graph it

View attachment 26274

In the above picture is an indication of domain and range, for y<1 and x<2, we have our domain and range specified for x<2 it is shaded in green, for y<1 it is shaded in blue, and the section cut off by the grey line is our domain and range, so in that sector the graph will be there.

Testing those large numbers you dont need to plot (though this can help alot too with determining shape), they help with the situation in number 3, in order for us to determine shape of the curve. For example if we put in a large positive value for say:
When we put in x=100, we get the answer as y=-9, so we know that as x goes further and further to infinity, our y value keeps decreasing and decreasing, however the y decreases at a 'slower' rate than x increases, so we demonstrate the curve as such.

Remember its not always negative infinity for square root functions, if negative infinity is outside the domain, test positive, if positive outside domain test negative infinity.

All in all I would not call plotting points a noob way of doing things, in reality the noob way would be to memorise how the curve looks like than rote how to translate the curve (up down left right etc) (im assuming this is what your friends do)

Wasn't it large negative values? Like I know you can't have a negative in a square root but is it easier to test large negative values?

How do you know if negative infinity is outside or inside the domain?

What's testing neg/pos infinity? is that the one where you test those random numbers?

Just to confirm the whole domain thing so lets say this question:



So the domain would be x is less than or equal to 1 right? because 1-1=0 and zero is the lowest number you can have in a root right?
So how would I find the range? is it just 0? because square root 1-1=0 which is 0?

So then I would test large negative numbers? say if I test x=-100 then it would be:

which is



what do I do next? is this how you do it? :S

 

[Fawun]

Re: Math help (Because Carrot made me do this)

oh, if no one else volunteers - i suppose i can do it

might as well. suggested it, might as well suggest myself

Do what? teach me?

 

[Shadowdude]

Re: Math help (Because Carrot made me do this)

Do what? teach me?

yeah

why, what did you think

 

[enoilgam]

Re: Math help (Because Carrot made me do this)

Graph



on its largest possible domain inside the interval .

That might be a challenge... I guess, if you really have nothing else, it can be worth doing in some situations. But obviously it should be a last resort kind of thing.

srsly fawun, the best way for you - i think - would be to arrange an in person meeting with someone knowledgeable to actually teach you graphing.

I think you would benefit from 1 on 1 help fawun.

 

[seanieg89]

Re: Math help (Because Carrot made me do this)

That might be a challenge... I guess, if you really have nothing else, it can be worth doing in some situations. But obviously it should be a last resort kind of thing.



I think you would benefit from 1 on 1 help fawun.

Yep. The graph I posted isn't too hard, but my point is anything that oscillates a lot makes plotting a few points next to useless.

 

[Fawun]

Re: Math help (Because Carrot made me do this)

That might be a challenge... I guess, if you really have nothing else, it can be worth doing in some situations. But obviously it should be a last resort kind of thing.



I think you would benefit from 1 on 1 help fawun.

No one will help me 1v1

My sister doesn't remember any of her maths
My tutor encourages r0te learning and i'm too scared to ask her.

 

[seanieg89]

Re: Math help (Because Carrot made me do this)

No one will help me 1v1

My sister doesn't remember any of her maths
My tutor encourages r0te learning and i'm too scared to ask her.

I honestly would be happy to in topics other than graphing, but graphing is so hard to convey when not in person, it would be easier to get someone like Carrot or actually SD to help you out.