Maths (1 Viewer)

drsabz101 · Jan 26, 2016

Q. How can I tell if a graph is a function or a relation , with just a drawing of it and nothing else. Do I draw a vertical line?

Shuuya · Jan 26, 2016

If the vertical line passes through the graph more than once, then the graph is a relation

If it passes through only once, then it is a function.

(i.e every x value much have one distinct y value for functions)

So the above graph is a function

drsabz101 · Jan 26, 2016

Okay thnx

InteGrand · Jan 26, 2016

By the way, every function is a relation, but not every relation is a function.

drsabz101 · Jan 26, 2016

Green Yoda · Jan 26, 2016

It is a function when there is only ONE permissible y value for EACH x value.
This is NOT true when vice versa.

InteGrand · Jan 26, 2016

Rathin said:
It is a function when there is only ONE permissible y value for EACH x value.
This is NOT true when vice versa.

$\noindent What do you mean by the \textit{vice versa} in this case?$

Nailgun · Jan 26, 2016

I assume he means you can have multiple x values per y value, like having two x-intercepts at y=0 in a parabola

si2136 · Jan 26, 2016

Vertical Line Test.

Green Yoda · Jan 26, 2016

InteGrand said:
$\noindent What do you mean by the \textit{vice versa} in this case?$

So for each y value (output) there can be more than 1 x value (input)

drsabz101 · Jan 26, 2016

I know what he means (e.g. like the graph of a circle)

InteGrand · Jan 26, 2016

Rathin said:
So for each y value (output) there can be more than 1 x value (input)

$\noindent Ah right, so you meant that if there's more than $y$-value for a certain $x$-value, it's not a function? Yeah, that's correct by definition of function.$

$\noindent Edit: Oh wait, you meant that a function is allowed to have more than one $x$-value map to a given $y$-value. Yes, this is also true. Such a function is called a \textit{many-to-one} function.$

InteGrand · Jan 26, 2016

drsabz101 said:
I know what he means (e.g. like the graph of a circle)

He was actually talking about functions (a circle graph doesn't represent a function).

Green Yoda · Jan 26, 2016

InteGrand said:
$\noindent Ah right, so you meant that if there's more than $y$-value for a certain $x$-value, it's not a function? Yeah, that's correct by definition of function.$

$\noindent Edit: oh wait, you meant that a function is allowed to have more than one $x$-value map to a given $y$-value. Yes, this is also true. Such a function is called a \textit{many-to-one} function.$

Yup, if there is more than one y value per x value then it's not a function as for yeah y value there must be only 1 x value but there can be more than 1 x value for each y value. I see it in a science way, the independent variable which is the x value or x coordinate must always be different. E.g (3,4) (4,4) is a function while (3,2) (3,5) is not.

Paradoxica · Jan 26, 2016

InteGrand said:
$\noindent Ah right, so you meant that if there's more than $y$-value for a certain $x$-value, it's not a function? Yeah, that's correct by definition of function.$

$\noindent Edit: Oh wait, you meant that a function is allowed to have more than one $x$-value map to a given $y$-value. Yes, this is also true. Such a function is called a \textit{many-to-one} function.$

$Also known as a \textbf{surjective} function$

Green Yoda · Jan 26, 2016

drsabz101 said:
I know what he means (e.g. like the graph of a circle)

It has more than 1 y value per x value so it's not a function. But a semi circle is a function.

InteGrand · Jan 26, 2016

Paradoxica said:
$Also known as a \textbf{surjective} function$

$\noindent Surjective is different, meaning that for every $b$ in the specified codomain of the function $f$, there exists an $a$ in its domain such that $f(a)=b$. The many-to-one property simply means that $f$ is a function that is not \textit{one-to-one} (another word for one-to-one is \textit{injective}).$

Paradoxica · Jan 26, 2016

InteGrand said:
$\noindent Surjective is different, meaning that for every $b$ in the specified codomain of the function $f$, there exists an $a$ in its domain such that $f(a)=b$. The many-to-one property simply means that $f$ is a function that is not \textit{one-to-one} (another word for one-to-one is \textit{injective}).$

That would pass through as non-injective.

axwe7 · Jan 26, 2016

Is this Geography?

leehuan · Jan 26, 2016

axwe7 said:
Is this Geography?

This is maths mr sarcasm

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