Question

explain domain and range of functions.. pls.

Answer 1

For example, for \(y=\sqrt{x}\), what can x be?

Answer 2

(a) Can it be 1?
(b) Can it be 0?
(c) Can it be -1?

Answer 3

IT COULD BE 1

Answer 4

sorry for the capslock hehe

Answer 5

xD

Answer 6

and the others?

Answer 7

(b) can it be 0?
(c) can it be -1?

Answer 8

cant be -1 cause it'll be imaginary

Answer 9

cant also be 0..

Answer 10

why not?

Answer 11

+ infinity?

Answer 12

sq rt of 0 is 0.

Answer 13

and?

Answer 14

... thats all?

Answer 15

nope

Answer 16

sorry

Answer 17

lemme draw up a small conclusion first:

If there is a function \(y=\sqrt{x}\), x can be positive or zero, but not negative.

Answer 18

don't say sorry lol it's not your fault :P

Answer 19

Therefore one can conclude that \(y=\sqrt{x}\)'s domain is [0,∞]

Answer 20

yes yes you're right.

Answer 21

get it?

Answer 22

braces?

Answer 23

pardon?

Answer 24

not [0, infinity)?

Answer 25

lol ok yes you're right, i'm not familiar with notation :P

Answer 26

haha how about range?

Answer 27

Now consider a function \(y=4x^2\).
(a) Can y be 1?
(b) Can y be 0?
(c) Can y be -1?

Answer 28

yes, it can be 1

Answer 29

all of the above

Answer 30

(a) For what value of x will y be 1?
(b) For what value of x will y be 0?
(c) For what value of x will y be -1?

Answer 31

Be aware that y is being asked now, not x.

Answer 32

(a) 1/2, (b) 0 and (c) --

Answer 33

well done.

Answer 34

(a) Can y be 1?
(b) Can y be 0?
(c) Can y be -1?

Answer 35

so its a and b?

Answer 36

exactly :)

Answer 37

Lemme draw a lil' conclusion:

Answer 38

For the function \(y=4x^2\), y can be 0 and positive, but not negative.

Therefore, one can colcude that \(y=4x^2\)'s range is [0,+∞).

Answer 39

wooh thank you. got it now.. no. not really. thank you so much!!

Answer 40

ok, i need to make you got it, so... what do you not understand? :)

Answer 41

the range its kinda tricky?

Answer 42

wait.. so this is your strategy in finding domain and range? *(a) Can it be 1?
(b) Can it be 0?
(c) Can it be -1?

Answer 43

Well, remember two things.
(i) Domain is related to the x-value, i.e. what x can be.
(ii) Range is related to the y-value, i.e. what y can be.

Answer 44

\(y=\sqrt{x}\) the range of this is [1, + infinity)?

Answer 45

x can be 0 :)

Answer 46

ah yes! tsk.

Answer 47

thank you thank you

Answer 48

no problem :)

Answer 49

always remember, domain->x, range->y

Answer 50

yes yes. thank you =)

Answer 51

no problem :D

Answer 52

\[y=\sqrt{1-x^2}\]

Answer 53

Find domain and range xP

Answer 54

[0, + inifinity) domain

Answer 55

nope :P

Answer 56

Can x be 2?

Answer 57

it'll be -3

Answer 58

it'll be \(\sqrt{-3}\)

Answer 59

\[y=\sqrt{1-x^2}\]

Answer 60

and?