Question

Identifying Graphical function

Answer 1

graph is


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

Answer 2

\(a\) is wrong because the graph is not symmetric about origin

\(b\) is wrong because the graph is not symmetric about \(y\) axis

Answer 3

i go wid \(c\)

Answer 4

but how did u concluded that

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

and also what is vertical line test

Answer 9

lets rephrase that question :

how do you know that the graph is a function ?

Answer 10

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

Answer 11

ok

Answer 12

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

Answer 13

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 \(\text{rama}\)

Answer 14

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

Answer 15

yes is below graph a function or just a relation

Answer 16

how do you know it

Answer 17

rellation but not function

Answer 18

cuz we have 2 different y values for same x value

Answer 19

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

Answer 20

ok i get that VLT

Answer 21

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

Answer 22

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

Answer 23

that means the function is defined only for x > 0

Answer 24

so it is undefined for x<0 ?

Answer 25

then it should be option d.)

Answer 26

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

Answer 27

ok i get that thanks

Answer 28

what about this graph

Answer 29

is it also option C.)

Answer 30

Yes

Answer 31

what about this graph

Answer 32

is is even