Question

Determine whether this equation defines y as a function of x
Please explain
@ganeshie8

Answer 1

where is the function ?

Answer 2

y^2=x-2
@ganeshie8

Answer 3

what exactly is needed for an equation to be qualified as function ?

Answer 4

heard of `vertical line test` before ?

Answer 5

For \(y\) to be a function of \(x\), every \(x\) value must point to exactly one \(y\) value :

\(\large y^2 = x-2 \implies y = \pm \sqrt{x-2}\)

Answer 6

Can tell me the value of y, when x = 3 ?

Answer 7

what exactly is needed for an equation to be qualified as function ? I'm not sure
Vertical test line..! No
+1, -1

Answer 8

what exactly is needed for an equation to be qualified as function ?
The value of y must be unique... but in terms of what?

Answer 9

That's a very good question !

Suppose you are `x`, do u have a girl friend ?

Answer 10

yes

Answer 11

good, lets say your girl friend is `y`

Answer 12

so, there must be one value only for y

Answer 13

here is the rule :
if you(x) have `only one` girlfriend(y), then your girl friend(y) is qualified to be called as a function of x

Answer 14

if you have more than one girl friend, then none of your girl friends can be called a function !

Pardon for the bad example lol, but u get the idea i hope... a graph would clear things up I guess... let me show you the graph of given equation :)

Answer 15

Np..!

Answer 16

Understood

Answer 17

Thanks

Answer 18

Look at the graph ^

for each x, there are two different possible y values - So y is not a function of x.

Answer 19

Thanks for the example
Another question:
Sketch graph of function
f(x)=x^2+4x+5
It can be expresses by completing the square
=(x+2)^2+1
Thegraph cuts y-axis when x=0, y=5
Then..

Answer 20

As x approach infinity, y approaches infinity
Similarly when x approaches - infinity, y approaches infinity
Why there's negative sign for ..

Answer 21

May be I'll answer the negative sign part after we sketch the curve :

step 1 : plot the vertex

Answer 22

I know how to sketch..
I'm just understand the negative infinity part