Question

For the following functions:

\[f(x) =4\] ( is this a function?)
\[x = (y+2)^{2}\]

• State the domain and range for each of your equations. Write them in interval notation.
• State whether each of the equations is a function or not giving your reasons for the answer.

Answer 1

are you asking if \(\large\sf\color{maroon}{ x=(y+2)^2 }\) is a function or
f(x)=4?

Answer 2

I'm asking for both expressions

Answer 3

@jim_thompson5910 @ganeshie8

Answer 4

@texaschic101 @Hero

Answer 5

please help me out

Answer 6

@iambatman

Answer 7

The first one is a function since it is a horizontal line y=4
Tge second you need to square root both sides
And subtract 2 from both sides . Then determine whether it is a function or not

Answer 8

@xapproachesinfinity what about the domain and range of a constant function ?

Answer 9

\[\sqrt{x}-2 =y\] is equivalent to:
\[x= (y+2)^{2}\]

Answer 10

a mean for the fist expression we have: [0,infinity)

Answer 11

but for the second i don't see any restriction..

Answer 12

@xapproachesinfinity

Answer 13

@radar @kropot72

Answer 14

The range of a horizontal line is a single point {4}
Fot the other one u need plus and minus sign
Be careful you are taking roots!

Answer 15

Oh I forgot the domain for the first one is all real numbers

Answer 16

lets put this in a clearer way:

f(x) = 4 --> domain infinity
range 4
is a function cause the vertical line proof ?

Answer 17

now for x = (y+2)^2

Answer 18

\[\sqrt{x}-2 = y\] I've given a lot of thought... this expression wouldn't be the inve

Answer 19

inverse of the original function ?

Answer 20

@tkhunny @dan815 please someone help me out

Answer 21

So what do think, I have already given the answer above when I said + or - root x

Answer 22

Im on the phone otherwise I would explain to you in details

Answer 23

mmm im just asking the reasons no the process..

Answer 24

The reason for plus or minus?

Answer 25

instead if i draw \[y =\sqrt{x}-2\]

Answer 26

No that's wrong!
what im saying is tha y=+-rootx-2
try to draw this one. not y=rootx-2

Answer 27

abviously you will have rootx-2 graph and the reflection of it over the x axis
it if you try the vertical line test then it is not a function

Answer 28

NO it is not wrong , graph the expression{x = (y+2)^2 give us:

Answer 29

ok now it good

Answer 30

i think now you have seen my point

Answer 31

do the test
if you draw y=+-rootx-2 you will have the same graph my friend because there is a reflection y=+-rootx-2 is two part y=rootx-2 and y=-rootx-2

Answer 32

it is the same thing doesn't matter how you approach it

Answer 33

a ok that's all i needed to know

Answer 34

but what about the vertical test line ?

Answer 35

if you do the vertical test you will see that is not a function

Answer 36

the vertical line cuts in more than one point

Answer 37

what is the domain of that relation?

Answer 38

So??

Answer 39

so i cannot graph this in that way, what if i change the axis it would work out

Answer 40

?

Answer 41

it is okay but just put in your mind that you change them