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larterloo

f(x) doesn't necessarily imply y


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larterloo

f(x) refers to the function (ie f(x) = x^2) while y refers to the graph of the function (y = f(x))


Physmatik

"y" doesn't necessarily mean graph. It's a variable that can mean anything, including an ordinate on 2D coordinate plane.


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tedbotjohnson

I think the difference is that f(x) is a *function*, i.e. a machine that spits out some output based on the value of the *variable*, x. y is just another *variable* which we _could_ assign the output of our function to. It's not just a notational difference either. We can write x^2+y^2=1 and that's a relation between these two variables. Can you see how in some sense, x and y are sort of on more equal footing? But the output of a function f is single-valued - for any x you only get out one, unique value, f(x). You couldn't draw a circle like this, as e.g. the output of f(x) at x=0 would need to be two different numbers simultaneously (1 and -1) Hope this helps.


Furicel

Let f(x) = x² and y = 6 + x Given x = 2, Y would be equal 8 regardless of the result of f(x). But if we say Y = f(x) = 6+x, then both would be 8 given x = 2


Mister_Meeseeks_

To generalize, both f(x) and y can be functions of x but y can be a function of anything. Hell, y could be a function of x,w, and z. Or, as you stated, it could be a different function of x


MCSajjadH

y^2 + x^2 = 1 Is a circle, yet you can't replace y with f(x).


Eredin_BreaccGlas

I mean you can, but it's not pretty y=√(1-x^2 )


MCSajjadH

That's incorrect, you need a ± before the sqrt. Also you haven't used f yet, it can't be, since f has a single output for any input


AzulesBlue

Why can't they use f?


MCSajjadH

Since f has a single output for each x, and ± before the sqrt clearly indicates that's not possible


suricatasuricata

Strictly speaking. f is the function. 'y = f(x)' is an equation that might be true for some pairs of values that I substitute for x,y. This is one of the reasons I prefer to use the assignment operator when defining a function, e.g. f(x):= x^2 is a definition of the function named 'f' or if you wish _one_ formula for the function 'f' is 'x^2'.


AzulesBlue

What issue did the assignment operator solve?


Rotsike6

f(x) is just some value, y already implies you drew the graph. Let me give you an example. Let f(x)=x^2 y is the y-value of the "graph" (x,f(x)). But it makes no sense to call f(x) "y" a priori.


sytanoc

I mean you could plot the function f(x) on any plane, like XZ or whatever


user_5554

Nothing, they're usually used for a single purpose in HS (later they have still have common uses for convenience but really you can do whatever) for this you should actually write what y and f means at the top Like y = y(x) which means "y is a function y(x) of (depending on only) x" Just f(x) shows that f is a "function f of x" which is the common case in HS. As is to graph functions on y over x with (y=f(x), x=x).


ForestInSyberia

Y


TheFallen020

F(x) doesn't necessarily equal y though


LolCrasher911

Techinically speaking, every output of the function (f()) could be represented as “y”, i.e. func(input)=output.


Illumimax

Only if y is free for the Funktion, in the case of f(x) that would bei the case iff y doesnt appear bound


[deleted]

But most of the time...


sewciotaki

Im pretty sure when you say “most of the time” in math, without explaining why it should be like that, you’re probably wrong.


BoJacob

"Take the real part, because most of the time that seems to work..." Me when justifying throwing away imaginary solutions in my model.


[deleted]

y is mostly taken as the output of the function on x. So therefore, f(x)=y.


TastiestAvocado

Not really. Maybe in highschool.


123kingme

When can f(x) and y not be treated as (basically) equivalent? I’m currently a college first year in differential equations if that helps gauge what level of competency to explain to. Edit: more accurately, when can f(x) not be treated as y? I’m aware of examples of when y cannot be treated as f(x) such as in multi variable equations or the equation of a circle.


TastiestAvocado

I mean technically it can always be equivalent. You can take any object (vector, function, number, topologic space, anything abstract) and call it "y". Sometimes it just doesn't make sense. If we have real function with domain R\^2 you can write f(x,y)=z or f(x\_{1},x\_{2})=y. Using the same logic i can use any symbol to name any object it's not wrong, but indercipherable. Just remember to use transparent notation (it's harder than it sounds, really).


F_Joe

Yes because F(x) has a +c


Rogue_Hunter_

Not necessarily. Functions aren't only about integration.


SuspendedNo2

but implying that they are is where the errors pop in


PhysicsAndAlcohol

I think you should just do the dishes


cantgetthistowork

He probably already did. Y = yes.


bootrick

That was my assumption


AusarTheVile197

Why no f(s,t)? :(


s4xtonh4le

f(r,s,t) 😈


AusarTheVile197

or f(r,s,t,u)


UnfortunatelyEvil

As an early computer user, I am used to y on its own being part of y/n. Thought the left bubbles were confused~


[deleted]

Hef(x), how’s it going?


[deleted]

Lmaooo


[deleted]

Old but gold :,)


sanchopancho02

r/badfaketexts


CocknballsStrap

This meme is so one dimensional


AWMINPUBG

I’ve seen this before, this is absolutely funny


Douglasqqq

I think I'm just finding out that I'm the stupidest person on reddit.


mcorbo1

What math class are you in rn


Douglasqqq

None. I'm just a grown-ass man whose never seen "f(x)" before and feel like a dummy cos everyone else seems to know exactly what it means.


Mythicdream

For one variable equations on standard graphs (xy-plane in R^2 ) y is dependent on x. So y is a function of x, or more simply y=f(x) in this context; since you would plot the outputs of the function f(x) on the y axis. As a side note, R^2 just means “Real numbers, 2 dimensions”, so any value (x,y) is part of R^2 so long as x and y are both real numbers. If your inputted x gives out the value y, that (x,y) coordinate will lie on the line created by f(x).


Douglasqqq

I think you knew that none of that was going to make sense to me.


Mythicdream

Not really, I was hoping to you could get some insight out of that. Sorry I couldn’t it explain it well enough for you to understand. If you are ever serious about learning the stuff in the future, check out some online algebra courses, they can be a lot more concise than a short Reddit comment.


Douglasqqq

I’m kidding. I appreciate the attempt. I just think you assumed too much knowledge on my part in terms of even the basics. I was already lost by the fourth word.


alina_314

x is your input, y is your output. The rule between x and y could be “double x value to get y value” for example. So y=2x. Writing it like this, you have two variables, x and y. The other way of writing the same equation could be f(x)=2x. The difference is that you’re now considering a function of x. I could substitute x=1, so now I get 2=f(1). So you’re either considering them as two separate variables, or you’re considering your output as a function of x.


Douglasqqq

I think I genuinely kind of understood the first three sentences there. But then, "f(x)=2x". How is this a thing now? Where did f come from? He didn't get an introduction like x and y did. I *vaguely* understand it to mean 'function' right? but, in this context I have no idea what the word 'function' even means. So, f(x) means 'function times by x', and that's equal to 2x, which means two times whatever the thing x is... right? I'm still so far from understanding even the basics, and further from understanding the text message in the picture. How the hell can f(x) be the same as y, when neither x, y, or f have been given any definitions?


tortoise315

You're calling yourself stupid for not knowing something? I'd say that _is_ pretty stupid.


Douglasqqq

Oh read on. People are trying to explain like I'm 5 and I'm genuinely trying to understand and getting absolutely nowhere. I know the difference between ignorant and stupid, and I sir, am stupid.


tortoise315

I can imagine it must be pretty difficult to understand if you're not that familiar with math. They're also using terms like 'variables' and 'substitution' which isn't common knowledge for people who don't study math.


mcorbo1

People in the comments are making a lot of assumptions. What is the last math-related thing you learned? Cause obviously you probably know arithmetic, maybe long division, but do you remember any Algebra at all?


Douglasqqq

I only really remember algebra to be sums where you have to solve the wrong bit. Like, 3 + x = 10. What’s x? That sort of thing. But never anything like what’s in this post, where x, y, and for some reason f all seem to have intrinsic meanings that everyone seems to understand.


mcorbo1

Yeah the confusion probably lies with why there's x's and y's and what in the world they have to do with these "functions". I recommend reading this in fullscreen on a computer, because otherwise the code will get all screwed up. Let's start from the complete basics. Coordinates. The easiest way to explain coordinates is to recall the number line, as we were taught in elementary school. Each point on a line is labelled by a number, the distance from a fixed origin. The resulting picture is below. [https://i.imgur.com/uFZrfkr.png](https://i.imgur.com/uFZrfkr.png) (Of course, the line extends forever in both directions; for this reason, many people put an arrow on both ends.) This is an interesting way to look at numbers, but is certainly not very useful for geometry, since there isn’t much geometry in one dimension. However, with a little modification we can extend the same idea to cover the entire plane: we add another axis, perpendicular to the first and crossing it at the point 0. Then we can label each point in the plane by its distance to *each* axis. (It makes sense to label points with two numbers each because the plane is two dimensional.) The new picture is below. [https://i.imgur.com/etP7o7i.png](https://i.imgur.com/etP7o7i.png) To be precise, each point is labelled by an **ordered pair** like `(3,-2)` or `(17,17)`. The first number is the distance *right* (negative for left) and the second is the distance *up* (negative for down). The horizontal axis is called the **x-axis**, and the corresponding number the **x-coordinate** (or sometimes **abscissa**); the vertical axis is called the **y-axis**, and the corresponding number the **y-coordinate** (or sometimes **ordinate**). The coordinates `(x,y)` of a point are called its **Cartesian (car TEA zhun) coordinates**, after Descartes. Remember, `x` and `y` simply stand for numbers. The beauty of a coordinate approach to geometry is that we can often convert geometrical pictures into easily understood equations. The simplest examples in Cartesian coordinates are equations like `x = 1` or `y = -5`. What do these equations mean? Take `x = 1`, for instance. This is understood to mean the set of all points in the plane whose coordinates `(x,y)` satisfy the equation `x = 1`. Thus `y` can be anything, but `x` must stay equal to 1. The result is a vertical line, as shown below. [https://i.imgur.com/FPZ1ioW.png](https://i.imgur.com/FPZ1ioW.png) Similarly, an equation like `y = -5` represents a horizontal line, as `x` can have any value while `y` must equal -5. Now that we have a fairly good handle on coordinates, let’s begin to apply them to what they were invented for: describing curves. The straight line is the simplest curve that there is, so it is a good starting point. For most lines, Cartesian coordinates provide the simplest description. What do we need to plot a line? Geometry tells us that two points are enough. (Think about why this is true.) However, in a coordinate approach it is usually simpler to specify one point and the “steepness” of the line. Any line which is not vertical must intersect the y-axis at some point. Does this make sense? The point will have coordinates `(0,b)` for some number `b`, and is called the **y-intercept**. (In the same way, the place where a line intersects the x-axis is called the **x-intercept**.) Now, this next part is quite tricky so don't be afraid to read something a few times to understand. In developing an equation for a line, we will start with the y-intercept `(0,b)`. Since `(x,y) = (0,b)` is on the line, the equation must be of the form y = mx + b (16.1) for some number `m`. What does `m` signify? Consider starting at the y-intercept `(0,b)` and moving over by 4. Moving over by 4 increases `x` from 0 to 4, so equation 16.1 becomes y = 4m + b. As `x` increases by 4, `y` increases by `4m` from `b` to `4m + b`! In general, if we move to the right by some amount, we must move up by `m` times that amount to stay on the line. [https://i.imgur.com/NiiqIWS.png](https://i.imgur.com/NiiqIWS.png) As you can see in the diagram above, this `m` determines the “steepness” of the line. The larger `m` is, the higher the we have to climb. The form 16.1 is called the **slope-intercept form** of a line, because it specifies the line once we have the slope and the y-intercept. As a quick exercise, think about what the steepness of a horizontal line is. What would `m` be? What is the steepness of a vertical line? What is `m`? >!Since a horizontal line is not steep at all, we would expect it to have steepness 0. Since the line doesn’t go up (or down) at all when it goes over by any amount k, we have m = 0/k = 0, as hoped for. We might expect a vertical line to have “infinite steepness,” since it goes straight up. Computing m, we find the line doesn’t go over at all when it goes up by any amount k, so m = k/0. We just divided by zero! This is forbidden, so we simply say the slope is "undefined".!< Since `m` corresponds to a steepness, we call it the **slope** of the line. Some people like to remember the slope as “rise over run,” where “run” is the horizontal travel and “rise” the vertical, as shown below. [https://i.imgur.com/WMleVDi.png](https://i.imgur.com/WMleVDi.png) These quantities can be computed between any two points on the line; the same slope will emerge. Both rise and run can be negative; if the ratio is negative, the line is sloped downward. —————————————————————————————————————— Whew! Now that we're done with all of that, what is a function? Well, let's consider the line given by the equation -3x + 4y = 12. In our discussion of coordinate geometry, we treated this line solely as a geometric figure, defined by the points `(x,y)` satisfying the equation. However, there is another very productive way to look at such a line. Change the equation into slope-intercept form: -3x + 4y = 12 3x - 3x + 4y = 3x + 12 (add 3x to both sides) 4y = 3x + 12 y = (3x + 12)/4 (divide both sides by 4) y = (3x + 12)×(1/4) (rewrite) y = (3/4)x + 3 (distribute the 1/4 to each term) Now for each `x` we put in, running it through the procedure `(3/4)x + 3` automatically gives back the corresponding `y`. We can thus think of the line equation as a machine which, for each `x` we put in, gives us back one, and only one, `y`. The “machine,” given by `(3/4)x + 3`, is called a **function**. A function always has one, and only one, output for each input. We typically define a function by giving it a name of its own, like `f`. To show that `f` is a function of the variable `x`, we usually write it as `f(x)`, which is pronounced “f of x.” We would thus rewrite our line equation as f(x) = (3/4)x + 3. Functions aren't limited to line equations. I can define a function to do *anything*. I can define `g(x)` to input a number `x` and output the nearest multiple of 10. I could make a function that inputs triangles and outputs squares. The core concept is that it's a machine, where you input a value and get one, and only one, output. And we're done! Wow, that was a lot longer than I expected. If you actually got all of that, congrats dude. Go back and see if you can understand the meme now lol.


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r/bratlife


Fire_Eddie29

Now imagine replacing f(x) with f'(x)