Functions | Mathematics | Page 1

rotund hollowBOT Feb 28, 2023, 7:11 AM

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misty pecanBOT Feb 28, 2023, 7:12 AM

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animeonfire

bleak pivot Feb 28, 2023, 7:12 AM

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no idea

hoary cipher Feb 28, 2023, 7:13 AM

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It's the same as saying y=x

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So if you are at 0 on your x-axis, then you must be at 0 on the y-axis as well.

bleak pivot Feb 28, 2023, 7:14 AM

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what do I do with 4?

hoary cipher Feb 28, 2023, 7:14 AM

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hoary cipher So if you are at 0 on your x-axis, then you must be at 0 on the y-axis as well.

The same goes for x=1, x=0.5, x=2, etc.

misty pecanBOT Feb 28, 2023, 7:16 AM

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animeonfire

hoary cipher Feb 28, 2023, 7:16 AM

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In other words, you slide f(x)=x four units up.

bleak pivot Feb 28, 2023, 7:17 AM

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I think I kinda get it

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is it like only vertical then?

twilit marsh Feb 28, 2023, 7:20 AM

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i think i might be able to help, you still here?

bleak pivot Feb 28, 2023, 7:20 AM

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yeah still here

twilit marsh Feb 28, 2023, 7:21 AM

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just so im 100% clear im going to explain all the details so forgive me if you know some of this already, so in the image you got the two lines at the center, up and down and left and right, the line that goes up and down is the y-axis and left to right is x-axis

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thats just termonology so dont worry too much

bleak pivot Feb 28, 2023, 7:22 AM

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clear so far

twilit marsh Feb 28, 2023, 7:22 AM

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so essentially your given the equation x+4

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and all its asking you to do is plot it which means put a line through some points

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to find those points all you have to do is plug in some values for x

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so lets say x=1

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then x+4 = 1+4

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so we know that somewhere something will relate to the number 5 on this graph, not sure where yet

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that all makes sense?

bleak pivot Feb 28, 2023, 7:24 AM

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uh sorta

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the other guy said it goes 'up' 4 four units up

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so is it vertical?

twilit marsh Feb 28, 2023, 7:25 AM

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yeah so he is refering to x=0 where 0+4=4, and the verticle part is the key idea, which i will explain

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so essentiall think about the x-axis and y-axis as number lines

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at the number 0 on the x numberline the y numberline will also have a value

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that value of the y number line when x=0 or the number 0 on the x numberline can be found with the equation x+4, where we just plug in our number, ie 0

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that might be confusing but does that make sense?

bleak pivot Feb 28, 2023, 7:29 AM

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it is confusing with so many 0's

twilit marsh Feb 28, 2023, 7:29 AM

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i bet i can explain it more visually

bleak pivot Feb 28, 2023, 7:30 AM

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not even those yt videos helped me

twilit marsh Feb 28, 2023, 7:30 AM

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ok so ignore the y-axis for now, pertend we only have the x-axis

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so here i have put a dot at the 0 position on the x numberline

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being at position 0 on the x-axis means that we will also be at another position on the y axis

bleak pivot Feb 28, 2023, 7:32 AM

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ohh I do know this

twilit marsh Feb 28, 2023, 7:32 AM

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anywhere on the 0 colum

bleak pivot Feb 28, 2023, 7:32 AM

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so there would be no slope here right?

twilit marsh Feb 28, 2023, 7:33 AM

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well if we were only thinking about this one colum, technically there would be no slope

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but thats not the main idea of this

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just understand, at any point on the x numberline, the y numberline also has a value on the same column

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so we want to find that y numberline point

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all you have to do, is put in what x column you are in, into the equation you were given

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so what x column are we in?

bleak pivot Feb 28, 2023, 7:35 AM

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I can only refer to quadrants I never heard of columns

twilit marsh Feb 28, 2023, 7:36 AM

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column is just a made up word, its not related to quandrants

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i just mean on this picture

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the "column" is where the blue line is

bleak pivot Feb 28, 2023, 7:36 AM

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4?

twilit marsh Feb 28, 2023, 7:36 AM

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at what position is that column on the x axis

bleak pivot Feb 28, 2023, 7:37 AM

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at 0 or 4

twilit marsh Feb 28, 2023, 7:37 AM

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4 would be

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and 0 would be

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so that makes sense right

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we arent thinking about the equation right now

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we will get to that

bleak pivot Feb 28, 2023, 7:38 AM

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right

twilit marsh Feb 28, 2023, 7:39 AM

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so just so im sure, can you tell me what column this picture is

bleak pivot Feb 28, 2023, 7:39 AM

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-1

twilit marsh Feb 28, 2023, 7:39 AM

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exactly

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alright now lets start thinking about the y-axis in this picture

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so the x column is at 0

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so to find the y value, how far up or down the column we want to go, we have to enter what column number we are in, in this picture we are in column 0, into the equation x+4

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how do we enter it you may be saying?

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simply set x to the column number

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does all of that make sense?

bleak pivot Feb 28, 2023, 7:42 AM

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still clear

twilit marsh Feb 28, 2023, 7:42 AM

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alright so entering column 0 into our equation, we would have 0+4

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thats equal to 4

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and THAT is how far up the column we need to go

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4 up

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does that make sense?

bleak pivot Feb 28, 2023, 7:43 AM

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still clear x2

twilit marsh Feb 28, 2023, 7:44 AM

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now all you have to do, is do that for every point on this graph, column -5 all the way to column 5

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so lets just try one for now, try to find how far up we would go for column 1

bleak pivot Feb 28, 2023, 7:45 AM

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would it be 4?

twilit marsh Feb 28, 2023, 7:45 AM

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and for reference this is the column at 1

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it wouldnt be 4 because to find how far the column we have to go up, we need to plug in the column number into the equation given

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x+4

bleak pivot Feb 28, 2023, 7:47 AM

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where am i trying to go?

twilit marsh Feb 28, 2023, 7:47 AM

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you are trying to figure out how far you need to go up the column at column position 1

bleak pivot Feb 28, 2023, 7:48 AM

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so moving up 4 units would be at 5

twilit marsh Feb 28, 2023, 7:49 AM

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exactly, we go 5 up this column because x+4 we plug in column 1 for x, 1+4=5

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thus 5 up

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now what about for -1?

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how far up do we have to go there

bleak pivot Feb 28, 2023, 7:50 AM

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-2 but I don't see this in the equation

twilit marsh Feb 28, 2023, 7:50 AM

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can you explain how u got -2

bleak pivot Feb 28, 2023, 7:51 AM

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moving 2 units to the left?

twilit marsh Feb 28, 2023, 7:51 AM

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well we are only thinking about the columns right now, im talking about the column at position -1

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so we arent worrying about left or right

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just how far up we need to go

bleak pivot Feb 28, 2023, 7:52 AM

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alr

twilit marsh Feb 28, 2023, 7:52 AM

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do you know how to find how far up to go?

bleak pivot Feb 28, 2023, 7:53 AM

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no i forgot again

twilit marsh Feb 28, 2023, 7:53 AM

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no worries

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all we do to find how far up or down we go is:

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take our column number

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here our column number is -1

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and plug it into the x value in the given equation

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the given equation is x+4

bleak pivot Feb 28, 2023, 7:54 AM

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ohh so its -1 + 4?

twilit marsh Feb 28, 2023, 7:54 AM

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yes

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so how far up do we go

bleak pivot Feb 28, 2023, 7:54 AM

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then it'd be 3

twilit marsh Feb 28, 2023, 7:54 AM

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exactly

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ok how about for column -2

bleak pivot Feb 28, 2023, 7:55 AM

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2

twilit marsh Feb 28, 2023, 7:55 AM

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yep

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that would look like that

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as we are at column -2

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and up 2

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so now just do that for every column

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which uve done most

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column -3 would be?

bleak pivot Feb 28, 2023, 7:56 AM

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1

twilit marsh Feb 28, 2023, 7:56 AM

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yep

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-4?

bleak pivot Feb 28, 2023, 7:57 AM

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0

twilit marsh Feb 28, 2023, 7:57 AM

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and -5

bleak pivot Feb 28, 2023, 7:57 AM

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-1

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ok

twilit marsh Feb 28, 2023, 7:57 AM

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yep, and that means we actually go below the column

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but yeah does that make sense?

bleak pivot Feb 28, 2023, 7:57 AM

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that part is clear thanks to you but i still have 1 last question

twilit marsh Feb 28, 2023, 7:57 AM

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yep?

bleak pivot Feb 28, 2023, 7:58 AM

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what does it mean by 'comparing the graph to the graph of f(x) = x'?

twilit marsh Feb 28, 2023, 7:58 AM

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so that means you are going to figure out all the points for both those graphs

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and then put them on the same graph

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so you would plot all the points of x+4 and x on this graph

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does that make sense?

bleak pivot Feb 28, 2023, 8:00 AM

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yeah totally

twilit marsh Feb 28, 2023, 8:00 AM

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oh and 1 thing i forgot to add

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you need to draw a line through all the points you plot

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so once you have put down all the points for 1 equation

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draw a line that goes through all of them

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and once you plot the other equation, draw a line that goes through all the points for the other equation

bleak pivot Feb 28, 2023, 8:01 AM

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oh yes we do that plenty with work

twilit marsh Feb 28, 2023, 8:01 AM

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alright sounds good

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any more questions?

bleak pivot Feb 28, 2023, 8:01 AM

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nope, thanks to you

twilit marsh Feb 28, 2023, 8:01 AM

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nw!

bleak pivot Feb 28, 2023, 8:01 AM

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now lemme figure out how to close this thing

twilit marsh Feb 28, 2023, 8:02 AM

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lol

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think you gotta type !close

bleak pivot Feb 28, 2023, 8:02 AM

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alr lemme try

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!close

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delete message?

twilit marsh Feb 28, 2023, 8:02 AM

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im wrong lol

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idk lol

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well i gotta go to sleep

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gl with closing it

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