Question

Hey guys help me out with this and it'll be vastly appreciated. :) Giving medals.

Answer 1

what's the question?

Answer 2

One sec

Answer 3

\[y = \sqrt{4-x} + 3\]

explain if its a function
find the domain
find the range

Answer 4

Can you help?

Answer 5

yes

Answer 6

well domain of a function is all the numbers that can be used in the function.perhaps in this function we can't find f(5) .

Answer 7

got it?

Answer 8

so 4-x must be larger or equal to0:
\[4 - x \ge 0\]

Answer 9

got it?

Answer 10

@SeverelyAutistic

Answer 11

Yes

Answer 12

well,did you get it?

Answer 13

\[4 - x \ge 0\]

Answer 14

Yea, is the vertical line test needed at all here?

Answer 15

so
\[x \le 4\]

Answer 16

it's the domain ;)

Answer 17

How would I know if its a function?

Answer 18

And yes thank you for the domain part I understood perfectly :D

Answer 19

you know this:

Answer 20

Don't think I do... could you explain?

Answer 21

you're welcome ;)
here if for two x we get the same f(x) it IS NOT a function.

Answer 22

Ahhh
So would I need to plug in values and check to see if they have the same results?

Answer 23

no it's not necessary.you can find if it's a function or not easily.
for example sqr (4-x) is cannot give us the same f(x) despite the Xs are different!

Answer 24

you get what am i saying?

Answer 25

Yep :D
So we got the domain, how about the range?

Answer 26

well,range is all the numbers the function give us! sqr (4-x) can give us at least 0 ... absolutely we cannot get -2 or -4 from sqr (4-x) !

Answer 27

ok?

Answer 28

Hm, so what you're saying is that sqr(4-X), you will always get a positive value, and thus it wouldn't satisfy the domain?

Answer 29

Took me a minute but I think I got it

Answer 30

is that it?

Answer 31

yes ;) sry i want to go...so the sqr (4-x) only give us 0,1,2 and etc...so we'll get at least 0 and we have 3 too, so we'll get at least 3 from the function...so the range is:
\[f(x) \ge 3\]

Answer 32

Or, in interval notation, the range is: [3, infinity)

Answer 33

Alright thank you so much, have a medal :)

Answer 34

you're welcome ;)

Answer 35

thanks for medal :)