Question

HELP!!!! WILL MEDAL AND FAN!!! .-.

Answer 1

hint:
the domain of a function \(y=f(x)\), is given by the set of all values of the variable \(x\)

Answer 2

and the range is given by the set of all values of the variable \(y\)

Answer 3

Oh?

Answer 4

I'm having trouble understanding :/

Answer 5

for example, if the values of \(x\), of a certain function, are:
\(1,2,3,4,5,6,7\) then the domain of this function is this set:
\({1,2,3,4,5,6,7}\)

Answer 6

All real numbers?

Answer 7

no, please this set:
\[domain = \left\{ {1,2,3,4,5,6,7} \right\}\]

Answer 8

uh....

Answer 9

now, the values of the variable \(x\) of the given function, are:
\(-4,-1,3,8\)
so, what is the domain?

Answer 10

6,4,2,3?

Answer 11

-3?*

Answer 12

no, such set is the \(range\) of the function, namely:
\[range = \left\{ {6,4,2, - 3} \right\}\]

Answer 13

Oh

Answer 14

The domain is 6,4,2,3,8?

Answer 15

domain is the set of all values of x
what are the values of variable \(x\)?

Answer 16

-4,-1,3,8

Answer 17

that's right, so the domain of the function is:
\[domain = \left\{ { - 4, - 1,3,8} \right\}\]

Answer 18

Thank you!

Answer 19

What about the bottom of the document?

Answer 20

numbers 2 and 3 are hard to understand :/

Answer 21

:)
ok!
now question #2
here we have a certain number of points

Answer 22

such points are:
\[\begin{gathered}
\left( {0,2} \right) \hfill \\
\left( { - 1,0} \right) \hfill \\
\left( {1,0} \right) \hfill \\
\left( { - 2, - 2} \right) \hfill \\
\left( {2, - 2} \right) \hfill \\
\end{gathered} \]

Answer 23

now, I ask, what are the values of the variable \(x\)?

Answer 24

2,1,-1,-2

Answer 25

for example, if I consider the first point: \((0,2)\), then the first entries, namely \(0\), is the value of \(x\): \(x=0\)

Answer 26

I think that also \(x=0\) is a value of x

Answer 27

Oh

Answer 28

so the domain, is:
\[domain = \left\{ { - 2, - 1,0,1,2} \right\}\]

Answer 29

Right

Answer 30

now I ask, what are the values of \(y\)?

Answer 31

-2,0,2

Answer 32

that's right! so we have:
\[range = \left\{ { - 2,0,2} \right\}\]

Answer 33

for third question, we have the list of value of the variable \(x\), as:
\(\{-1,0,4\}\)

Answer 34

values*

Answer 35

whereas the list of the values of variable \(y\), is:
\[\left\{ { - 3,1,2} \right\}\]

Answer 36

So I need to put them in their places?

Answer 37

we have to associate to each value of x, one and \(only\) one value of y

Answer 38

for example, I start with this point:
\[\left( { - 1, - 3} \right)\]

Answer 39

now please write another ordered pair using \(x=0\) and \(y=2\)

Answer 40

it is \((0,2)\)
finally another ordered pair is \((4,1)\)

Answer 41

so I just write next to the graph... x=0 and y=2?

Answer 42

yes! you have to draw, these points:
\[\begin{gathered}
\left( { - 1, - 3} \right) \hfill \\
\left( {0,2} \right) \hfill \\
\left( {4,1} \right) \hfill \\
\end{gathered} \]

Answer 43

Well I wrote it next to the graph and im not sure how to draw onto it

Answer 44

it wont really let me :/

Answer 45

I plotted points I guess

Answer 46

yes!
here is the first point:

Answer 47

of course, you can add other points, nevertheless, please make attention, you have to associate to each value of x, one and only one value of y, namely you can not choose both these ordered pairs:
\((4,1)\) and \((4,2)\)
you can choose only one of them

Answer 48

Well I chose (4,1)

Answer 49

ok!

Answer 50

Is it okay?

Answer 51

yes!

Answer 52

am I done?

Answer 53

please add this point:
\((0,2)\)

Answer 54

Already have :)

Answer 55

And I added (-1,-3)

Answer 56

Should I remove it?

Answer 57

no,
the points are:
\[\begin{gathered}
\left( { - 1, - 3} \right) \hfill \\
\left( {0,2} \right) \hfill \\
\left( {4,1} \right) \hfill \\
\end{gathered} \]
and we have finished

Answer 58

Thank you so much. If it weren't for you I would have been stuck on this forever :)

Answer 59

:)