Identifying Graphical function

- mathmath333

Identifying Graphical function

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- mathmath333

|dw:1435071288021:dw|

- mathmath333

graph is
\(\large \color{black}{\begin{align} &a.) \ f(x)=-f(x) \hspace{.33em}\\~\\
&b.) \ f(x)=f(-x) \hspace{.33em}\\~\\
&c.) \ \normalsize \text{neither even nor odd function} \hspace{.33em}\\~\\
&d.) \ f(x)\ \normalsize \text{doesn't exist at atleast one point of the domain.} \hspace{.33em}\\~\\
\end{align}}\)

- ganeshie8

\(a\) 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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## More answers

- ganeshie8

i go wid \(c\)

- mathmath333

but how did u concluded that

- ganeshie8

the graph passes vertical line test, so it is actually a function. so \(d\) is also wrong.

- ganeshie8

or are you asking how to conclude it is not symmetric about origin ?

- mathmath333

i mean how u judged that the function exists at all points ?

- mathmath333

and also what is vertical line test

- ganeshie8

lets rephrase that question :
how do you know that the graph is a function ?

- ganeshie8

it is essential to know the difference between a "relation" and a "function"

- mathmath333

ok

- ganeshie8

relation is just about anything,
for example : the relation showing friends of a student in your class is a relation
\[\{\text{(suresh, krishna), (rajesh, mahes), (suresh, rama), }\cdots\}\]

- ganeshie8

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 \(\text{rama}\)

- mathmath333

ok i get that relation can have multiple x values for y , but a function cannot

- ganeshie8

yes is below graph a function or just a relation
|dw:1435073159068:dw|

- ganeshie8

how do you know it

- mathmath333

rellation but not function

- mathmath333

cuz we have 2 different y values for same x value

- ganeshie8

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

- ganeshie8

|dw:1435073363932:dw|

- mathmath333

ok i get that VLT

- ganeshie8

lets get back to the actual graph, is it passing vertical line test ?

- ganeshie8

|dw:1435073452344:dw|

- mathmath333

yes it passes VLT but for negative values of x there is not y values such as this line

- mathmath333

|dw:1435073568393:dw|

- ganeshie8

that means the function is defined only for x > 0

- mathmath333

so it is undefined for x<0 ?

- mathmath333

then it should be option d.)

- ganeshie8

x<0 is not part of the domain, so d is wrong.

- mathmath333

ok i get that thanks

- mathmath333

what about this graph |dw:1435074083721:dw|

- mathmath333

is it also option C.)

- ganeshie8

Yes

- mathmath333

|dw:1435074325926:dw|
what about this graph

- mathmath333

is is even

- ganeshie8

Yes notice that it is symmetric about \(y\) axis
|dw:1435074436000:dw|

- ganeshie8

\[\large f(x) = f(-x)\]

- mathmath333

|dw:1435074719834:dw|

- mathmath333

is it option d.)

- ganeshie8

nope, it is a function
check whether it is odd/even

- mathmath333

but it fails vertical line test at \(x=0\) ?

- ganeshie8

why ?
it is well defined at x = 0
f(0) = 0 right ?

- mathmath333

and what about the points |dw:1435075038716:dw|

- ganeshie8

look at the graph like this :
|dw:1435075017594:dw|

- mathmath333

but that graph u draw looks different from the original one

- ganeshie8

f(0) = 0
all other points are not part of the graph because the question clearly says f(x) = 0 at x=0

- mathmath333

ok

- mathmath333

so it is odd function

- ganeshie8

Yes how did u figure out it is odd ?

- mathmath333

because it is symmetrical with respect to origin

- mathmath333

is the reason correct

- ganeshie8

Yep!
|dw:1435075546512:dw|

- mathmath333

|dw:1435075812493:dw|

- mathmath333

this is option C

- ganeshie8

does it pass vertical line test ?

- mathmath333

no it should be option d.

- mathmath333

|dw:1435075996061:dw|

- mathmath333

this is option c.)

- ganeshie8

does it pass vertical line test ?

- ganeshie8

|dw:1435076100827:dw|

- mathmath333

lol no it doesnt pass

- ganeshie8

so that graph does not represent a function

- mathmath333

|dw:1435076275748:dw|

- mathmath333

this is odd function ?

- ganeshie8

Yes

- mathmath333

do i need to check further if equation of the graph is given

- dan815

id go with C too

- dan815

the function can do anything beyond what u dont see so u cant say its undefined at some domain

- dan815

|dw:1435076708335:dw|

- dan815

what u do know is that its not mirrored across the y axis or x and y axis

- dan815

|dw:1435076754260:dw|

- mathmath333

but this works fine so far (looks odd function)
https://www.desmos.com/calculator/zenrcqo1cg

- ganeshie8

|dw:1435076810329:dw|

- mathmath333

oh i see that is neat trick

- mathmath333

|dw:1435077093925:dw|

- ganeshie8

lets change option d to a more meaningful one :
d) not a function. only a relation.

- mathmath333

|dw:1435077115505:dw|

- ganeshie8

im not so comfortable with the phrase : "f(x) doesn't exist..."

- mathmath333

|dw:1435077115505:dw|

- ganeshie8

|dw:1435077393446:dw|

- mathmath333

|dw:1435077588951:dw|
ok this looks odd function

- mathmath333

f(x)=f(-x)

- mathmath333

|dw:1435077669264:dw|
this too is odd function ?

- ganeshie8

Yes

- mathmath333

|dw:1435077791382:dw|
this is which type of function

- mathmath333

this looks odd for me

- ganeshie8

sure ?

- mathmath333

yes,why ?

- ganeshie8

it is not an odd function
\[\large f(x) =\lfloor x\rfloor\]

- ganeshie8

Is below really true ?\[\large \lfloor x\rfloor =-\lfloor -x\rfloor \] ?

- mathmath333

this is greatest integer function ?

- ganeshie8

looks like it

- ganeshie8

|dw:1435078161945:dw|

- mathmath333

\(\large{ \lfloor 2.5\rfloor=2\\
-\lfloor -2.5\rfloor=-\lfloor 2\rfloor}=-2 \)
so this looks odd if it is GIF

- mathmath333

|dw:1435078351737:dw|

- ganeshie8

are you sure \(\large \lfloor -2.5\rfloor = -2\) ?

- mathmath333

yes the greatest integer function specifies that \(\lfloor x\rfloor\) will be equal to the smallest integer neighbouring to it.|dw:1435079336656:dw|

- ganeshie8

\(\large \lfloor -2.5\rfloor = -3\)

- ganeshie8

-3 is the smallest neighbor integer for -2.5

- xapproachesinfinity

how do you plot floor and ceiling with goegebra or some other programs

- xapproachesinfinity

i got it you just right floor :)

- ganeshie8

yes `f(x)=floor(x)` works just fine :)

- xapproachesinfinity

it does not let me do f(x)=floor(x)+x for example

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