Question

Determine whether the equation defines y as a function of x.

y = -x
Select one:
a. Yes
b. No
c. Not enough information.

Answer 1

For an equation to be defined as a function of x, it simply needs to contain that variable. So does y = -x, have an x in it?

Answer 2

yes it does, so it is a function of x

Answer 3

exactly!

Answer 4

Can you help me with the rest? I'm super confused

Answer 5

sure

Answer 6

Do i type them in here?

Answer 7

sure some people care about the "medals" but I am not about so type away!

Answer 8

that totally didn't come out right but that doesn't matter, lets ignore the answers for now.

Answer 9

okay

Answer 10

so do you know what a range of a function is?

Answer 11

the hightest and lowest numbers?

Answer 12

yes! but more specifically it is the range of values that y/f(x) can be! So do you have any idea about this function's particular range?

Answer 13

Ummmm. It would be all of it's y values

Answer 14

yes and what are the possible values for y?

Answer 15

btw if you don't understand or get confused tell me! I will try to explain it in a different way.

Answer 16

sorry lost connection

Answer 17

all values above y, since the +2 is present?

Answer 18

hmmm I let's think about it in a different way, I think I might have confused you. Let me instead as you a series of questions about the function.
Can y be a really big number?

Answer 19

ughh no it can't

Answer 20

why not?

Answer 21

if x is a really big number wouldn't that make y a really big number as well?

Answer 22

So if x can be a big number then y can as well, is that right? so in this case x has the potential to be a big number so that means y can as well

Answer 23

yes exactly so you agree that y can be a really big number?

Answer 24

yes!

Answer 25

Good so since it can be an infinitely large number we say that it's range can go all the way to positive infinity. Does that make sense, I might have phrased it weirdly?

Answer 26

no i get it. it would have the infinity sign on the right, in the y's spot with the round bracket? ) ∞

Answer 27

[2, positive infinity symbol)?

Answer 28

Nice good, now we must ask the opposite question! Whether is can be an extremely small number (aka a big negative number).

Answer 29

ohhh im not sure. Im guessing that it could be, if x can be any high number then it can be any low number as well, same goes for y.

Answer 30

EXACTLY!!!! Good! so if your thinking is correct what is the range of this function?

Answer 31

(negative inifity symbol, positive infinity symbol) ?

Answer 32

DING DING DING! yes 100% correct!

Answer 33

\[(-\infty,\infty)\]

Answer 34

btw do you know the difference between [] and () is?

Answer 35

I got the infity sign to work :P

Answer 36

nice!

Answer 37

i think i remember

Answer 38

the [] means something like its a set number and can't go above or below it?

Answer 39

eh sorta, it means that it's inclusive so if the function's range was [2,5), it would mean that the function range includes 2 but not 5. And of course everything between those two numbers.

Answer 40

make sense?

Answer 41

No problem, I really enjoy helping people which is why I do this!

Answer 42

Thanks again!! Is there a way to private message on here?

Answer 43

yes but it's not really helpful if you want to talk on it lol. You can just say it here, i'm sure no one will disturb us lol.

Answer 44

so do you know what local maximums and minimum are?

Answer 45

maximum would be the