Identifying Graphical function

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Identifying Graphical function

Mathematics
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|dw:1435071288021:dw|
graph is \(\large \color{black}{\begin{align} &a.) \ f(x)=-f(x) \hspace{.33em}\\~\\ &b.) \ f(x)=f(-x) \hspace{.33em}\\~\\ &c.) \ \normalsize \text{neither even nor odd function} \hspace{.33em}\\~\\ &d.) \ f(x)\ \normalsize \text{doesn't exist at atleast one point of the domain.} \hspace{.33em}\\~\\ \end{align}}\)
\(a\) is wrong because the graph is not symmetric about origin \(b\) is wrong because the graph is not symmetric about \(y\) axis

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Other answers:

i go wid \(c\)
but how did u concluded that
the graph passes vertical line test, so it is actually a function. so \(d\) is also wrong.
or are you asking how to conclude it is not symmetric about origin ?
i mean how u judged that the function exists at all points ?
and also what is vertical line test
lets rephrase that question : how do you know that the graph is a function ?
it is essential to know the difference between a "relation" and a "function"
ok
relation is just about anything, for example : the relation showing friends of a student in your class is a relation \[\{\text{(suresh, krishna), (rajesh, mahes), (suresh, rama), }\cdots\}\]
A function is also relation in which every input points to exactly one output. Above relation is NOT a function because \(\text{suresh}\) is pointing to two different students \(\text{krishna}\) and \(\text{rama}\)
ok i get that relation can have multiple x values for y , but a function cannot
yes is below graph a function or just a relation |dw:1435073159068:dw|
how do you know it
rellation but not function
cuz we have 2 different y values for same x value
that is also called vertical line test, sweep a vertical line from left to right if the graph touches the vertical line at two different places, then the graph is not a function
|dw:1435073363932:dw|
ok i get that VLT
lets get back to the actual graph, is it passing vertical line test ?
|dw:1435073452344:dw|
yes it passes VLT but for negative values of x there is not y values such as this line
|dw:1435073568393:dw|
that means the function is defined only for x > 0
so it is undefined for x<0 ?
then it should be option d.)
x<0 is not part of the domain, so d is wrong.
ok i get that thanks
what about this graph |dw:1435074083721:dw|
is it also option C.)
Yes
|dw:1435074325926:dw| what about this graph
is is even
Yes notice that it is symmetric about \(y\) axis |dw:1435074436000:dw|
\[\large f(x) = f(-x)\]
|dw:1435074719834:dw|
is it option d.)
nope, it is a function check whether it is odd/even
but it fails vertical line test at \(x=0\) ?
why ? it is well defined at x = 0 f(0) = 0 right ?
and what about the points |dw:1435075038716:dw|
look at the graph like this : |dw:1435075017594:dw|
but that graph u draw looks different from the original one
f(0) = 0 all other points are not part of the graph because the question clearly says f(x) = 0 at x=0
ok
so it is odd function
Yes how did u figure out it is odd ?
because it is symmetrical with respect to origin
is the reason correct
Yep! |dw:1435075546512:dw|
|dw:1435075812493:dw|
this is option C
does it pass vertical line test ?
no it should be option d.
|dw:1435075996061:dw|
this is option c.)
does it pass vertical line test ?
|dw:1435076100827:dw|
lol no it doesnt pass
so that graph does not represent a function
|dw:1435076275748:dw|
this is odd function ?
Yes
do i need to check further if equation of the graph is given
id go with C too
the function can do anything beyond what u dont see so u cant say its undefined at some domain
|dw:1435076708335:dw|
what u do know is that its not mirrored across the y axis or x and y axis
|dw:1435076754260:dw|
but this works fine so far (looks odd function) https://www.desmos.com/calculator/zenrcqo1cg
|dw:1435076810329:dw|
oh i see that is neat trick
|dw:1435077093925:dw|
lets change option d to a more meaningful one : d) not a function. only a relation.
|dw:1435077115505:dw|
im not so comfortable with the phrase : "f(x) doesn't exist..."
|dw:1435077115505:dw|
|dw:1435077393446:dw|
|dw:1435077588951:dw| ok this looks odd function
f(x)=f(-x)
|dw:1435077669264:dw| this too is odd function ?
Yes
|dw:1435077791382:dw| this is which type of function
this looks odd for me
sure ?
yes,why ?
it is not an odd function \[\large f(x) =\lfloor x\rfloor\]
Is below really true ?\[\large \lfloor x\rfloor =-\lfloor -x\rfloor \] ?
this is greatest integer function ?
looks like it
|dw:1435078161945:dw|
\(\large{ \lfloor 2.5\rfloor=2\\ -\lfloor -2.5\rfloor=-\lfloor 2\rfloor}=-2 \) so this looks odd if it is GIF
|dw:1435078351737:dw|
are you sure \(\large \lfloor -2.5\rfloor = -2\) ?
yes the greatest integer function specifies that \(\lfloor x\rfloor\) will be equal to the smallest integer neighbouring to it.|dw:1435079336656:dw|
\(\large \lfloor -2.5\rfloor = -3\)
-3 is the smallest neighbor integer for -2.5
how do you plot floor and ceiling with goegebra or some other programs
i got it you just right floor :)
yes `f(x)=floor(x)` works just fine :)
it does not let me do f(x)=floor(x)+x for example

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