mathmath333
  • mathmath333
Identifying Graphical function
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
mathmath333
  • mathmath333
|dw:1435071288021:dw|
mathmath333
  • 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
  • ganeshie8
\(a\) is wrong because the graph is not symmetric about origin \(b\) is wrong because the graph is not symmetric about \(y\) axis

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

ganeshie8
  • ganeshie8
i go wid \(c\)
mathmath333
  • mathmath333
but how did u concluded that
ganeshie8
  • ganeshie8
the graph passes vertical line test, so it is actually a function. so \(d\) is also wrong.
ganeshie8
  • ganeshie8
or are you asking how to conclude it is not symmetric about origin ?
mathmath333
  • mathmath333
i mean how u judged that the function exists at all points ?
mathmath333
  • mathmath333
and also what is vertical line test
ganeshie8
  • ganeshie8
lets rephrase that question : how do you know that the graph is a function ?
ganeshie8
  • ganeshie8
it is essential to know the difference between a "relation" and a "function"
mathmath333
  • mathmath333
ok
ganeshie8
  • 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
  • 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
  • mathmath333
ok i get that relation can have multiple x values for y , but a function cannot
ganeshie8
  • ganeshie8
yes is below graph a function or just a relation |dw:1435073159068:dw|
ganeshie8
  • ganeshie8
how do you know it
mathmath333
  • mathmath333
rellation but not function
mathmath333
  • mathmath333
cuz we have 2 different y values for same x value
ganeshie8
  • 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
  • ganeshie8
|dw:1435073363932:dw|
mathmath333
  • mathmath333
ok i get that VLT
ganeshie8
  • ganeshie8
lets get back to the actual graph, is it passing vertical line test ?
ganeshie8
  • ganeshie8
|dw:1435073452344:dw|
mathmath333
  • mathmath333
yes it passes VLT but for negative values of x there is not y values such as this line
mathmath333
  • mathmath333
|dw:1435073568393:dw|
ganeshie8
  • ganeshie8
that means the function is defined only for x > 0
mathmath333
  • mathmath333
so it is undefined for x<0 ?
mathmath333
  • mathmath333
then it should be option d.)
ganeshie8
  • ganeshie8
x<0 is not part of the domain, so d is wrong.
mathmath333
  • mathmath333
ok i get that thanks
mathmath333
  • mathmath333
what about this graph |dw:1435074083721:dw|
mathmath333
  • mathmath333
is it also option C.)
ganeshie8
  • ganeshie8
Yes
mathmath333
  • mathmath333
|dw:1435074325926:dw| what about this graph
mathmath333
  • mathmath333
is is even
ganeshie8
  • ganeshie8
Yes notice that it is symmetric about \(y\) axis |dw:1435074436000:dw|
ganeshie8
  • ganeshie8
\[\large f(x) = f(-x)\]
mathmath333
  • mathmath333
|dw:1435074719834:dw|
mathmath333
  • mathmath333
is it option d.)
ganeshie8
  • ganeshie8
nope, it is a function check whether it is odd/even
mathmath333
  • mathmath333
but it fails vertical line test at \(x=0\) ?
ganeshie8
  • ganeshie8
why ? it is well defined at x = 0 f(0) = 0 right ?
mathmath333
  • mathmath333
and what about the points |dw:1435075038716:dw|
ganeshie8
  • ganeshie8
look at the graph like this : |dw:1435075017594:dw|
mathmath333
  • mathmath333
but that graph u draw looks different from the original one
ganeshie8
  • 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
  • mathmath333
ok
mathmath333
  • mathmath333
so it is odd function
ganeshie8
  • ganeshie8
Yes how did u figure out it is odd ?
mathmath333
  • mathmath333
because it is symmetrical with respect to origin
mathmath333
  • mathmath333
is the reason correct
ganeshie8
  • ganeshie8
Yep! |dw:1435075546512:dw|
mathmath333
  • mathmath333
|dw:1435075812493:dw|
mathmath333
  • mathmath333
this is option C
ganeshie8
  • ganeshie8
does it pass vertical line test ?
mathmath333
  • mathmath333
no it should be option d.
mathmath333
  • mathmath333
|dw:1435075996061:dw|
mathmath333
  • mathmath333
this is option c.)
ganeshie8
  • ganeshie8
does it pass vertical line test ?
ganeshie8
  • ganeshie8
|dw:1435076100827:dw|
mathmath333
  • mathmath333
lol no it doesnt pass
ganeshie8
  • ganeshie8
so that graph does not represent a function
mathmath333
  • mathmath333
|dw:1435076275748:dw|
mathmath333
  • mathmath333
this is odd function ?
ganeshie8
  • ganeshie8
Yes
mathmath333
  • mathmath333
do i need to check further if equation of the graph is given
dan815
  • dan815
id go with C too
dan815
  • dan815
the function can do anything beyond what u dont see so u cant say its undefined at some domain
dan815
  • dan815
|dw:1435076708335:dw|
dan815
  • dan815
what u do know is that its not mirrored across the y axis or x and y axis
dan815
  • dan815
|dw:1435076754260:dw|
mathmath333
  • mathmath333
but this works fine so far (looks odd function) https://www.desmos.com/calculator/zenrcqo1cg
ganeshie8
  • ganeshie8
|dw:1435076810329:dw|
mathmath333
  • mathmath333
oh i see that is neat trick
mathmath333
  • mathmath333
|dw:1435077093925:dw|
ganeshie8
  • ganeshie8
lets change option d to a more meaningful one : d) not a function. only a relation.
mathmath333
  • mathmath333
|dw:1435077115505:dw|
ganeshie8
  • ganeshie8
im not so comfortable with the phrase : "f(x) doesn't exist..."
mathmath333
  • mathmath333
|dw:1435077115505:dw|
ganeshie8
  • ganeshie8
|dw:1435077393446:dw|
mathmath333
  • mathmath333
|dw:1435077588951:dw| ok this looks odd function
mathmath333
  • mathmath333
f(x)=f(-x)
mathmath333
  • mathmath333
|dw:1435077669264:dw| this too is odd function ?
ganeshie8
  • ganeshie8
Yes
mathmath333
  • mathmath333
|dw:1435077791382:dw| this is which type of function
mathmath333
  • mathmath333
this looks odd for me
ganeshie8
  • ganeshie8
sure ?
mathmath333
  • mathmath333
yes,why ?
ganeshie8
  • ganeshie8
it is not an odd function \[\large f(x) =\lfloor x\rfloor\]
ganeshie8
  • ganeshie8
Is below really true ?\[\large \lfloor x\rfloor =-\lfloor -x\rfloor \] ?
mathmath333
  • mathmath333
this is greatest integer function ?
ganeshie8
  • ganeshie8
looks like it
ganeshie8
  • ganeshie8
|dw:1435078161945:dw|
mathmath333
  • mathmath333
\(\large{ \lfloor 2.5\rfloor=2\\ -\lfloor -2.5\rfloor=-\lfloor 2\rfloor}=-2 \) so this looks odd if it is GIF
mathmath333
  • mathmath333
|dw:1435078351737:dw|
ganeshie8
  • ganeshie8
are you sure \(\large \lfloor -2.5\rfloor = -2\) ?
mathmath333
  • 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
  • ganeshie8
\(\large \lfloor -2.5\rfloor = -3\)
ganeshie8
  • ganeshie8
-3 is the smallest neighbor integer for -2.5
xapproachesinfinity
  • xapproachesinfinity
how do you plot floor and ceiling with goegebra or some other programs
xapproachesinfinity
  • xapproachesinfinity
i got it you just right floor :)
ganeshie8
  • ganeshie8
yes `f(x)=floor(x)` works just fine :)
xapproachesinfinity
  • xapproachesinfinity
it does not let me do f(x)=floor(x)+x for example

Looking for something else?

Not the answer you are looking for? Search for more explanations.