Question

Does the data in this table represent a function?

Input
(x) 3 7 11 15

Output
(y) 4 6 8 10

Answer 1

as long as the first numbers are all different, the answer is YES a function
ignore the y's completely

Answer 2

what would it look like as a function?

Answer 3

just as you see it, the table

Answer 4

you could also make ordered pairs \[\{3,4),(7,6),(11,8),(15,10)\}\]

Answer 5

f(x) = 3x + 4 ? is this right?

Answer 6

not hardly

Answer 7

if it was \(f(x)=3x+4\) then the y value would be 4 more than 3 times the x valuie

Answer 8

so here you have \((3,4)\) as pair, that means \[f(3)=4\]

Answer 9

i know there this a difference of 4 in the x outputs

Answer 10

looks to me like each output increases by 2, not by 4

Answer 11

it is the inputs that are increasing by 4 each time

Answer 12

lets back up a second
this is the entire question
Does the data in this table represent a function?
right?

Answer 13

oh yeah sorry, its the x inputs

Answer 14

there are 3 parts to the question, this is the first part

Answer 15

in the next part they ask to "Compare the data in the table with the relation f(x) = 5x – 21. Which relation has a greater value when x = 11?"

Answer 16

ok well that part only asks "function, yes/no"
it does not ask you to find a rule for the function
all you need to see is that all the x values are different, then you answer YES

Answer 17

ok

Answer 18

in part A, they asked me to justify my answer.

Answer 19

ok if \[f(x)=5x-21\] do you know how to find \(f(11)\)?

Answer 20

no

Answer 21

justify your answer "all the x values are distinct (different)"

Answer 22

ok "no" is a fine answer

Answer 23

\[f(x)=5x-21\\
f(\xi)=5\xi -21\\
f(\spadesuit)=5\spadesuit-21\\
f(11)=?\]

Answer 24

I don't know.

Answer 25

\[f(11)=5\times 11-21=?\]

Answer 26

55-21 =34

Answer 27

yes that is what i get too

Answer 28

and what is the y value from the table that corresponds to the x value of 11?

Answer 29

ok thank you.

Answer 30

8?

Answer 31

yes

Answer 32

now you can answer
in the next part they ask to "Compare the data in the table with the relation f(x) = 5x – 21. Which relation has a greater value when x = 11?"
easily enough, since one output is 8 (from the table) and the other output is 34

Answer 33

they ask to turn the data in the table into a function, and compare it to f(x) = 5x - 21. I don't know what the function is from the data in the table. I need help to figure that out

Answer 34

aren't the ordered pairs good enough, or do you need a rule?

Answer 35

i think i need a function like f(x) = 5x - 21 to compare it to

Answer 36

ordered pairs look like\[\{(3,4),(7,6),(11,8),(15,10)\}\]
rule looks like \[g(x)=sommat\]

Answer 37

but i don't know how to make a function from that table

Answer 38

ok that is going to require some work

Answer 39

you already said the x values increase each time by 4 right?

Answer 40

and i said the y values increase by 2
that means this is a line, and the slope of the line that goes "right 4, up 2" is \[\large \frac{2}{4}=\frac{1}{2}\]

Answer 41

yes

Answer 42

so it is going to look like \[g(x)=\frac{1}{2}x+b\] now you need \(b\)

Answer 43

ok so that is the slope?

Answer 44

yes

Answer 45

right 4 , up 2 slope is 2/4

Answer 46

ok

Answer 47

but i think it has to start like this: f(x) = 1/2 + or - another number.

Answer 48

it is going to be \[g(x)=\frac{1}{2}x+ number\]

Answer 49

okay this is part b:
Part B: Compare the data in the table with the relation f(x) = 5x – 21. Which relation has a greater value when x = 11?

so far, i did this:

f(x) = 5x - 21
f(11) = 5 x 11 - 21
f(11) = 55 - 21 = 34.
f(11) = 34.

Answer 50

i think now i need to make a relation from the table and compare it to f(11)= 34.

Answer 51

no you do not

Answer 52

i don't know what to do

Answer 53

in the table, the y value for 11 is 8
in the function the y value for 11 is 34
they ask you which is bigger
i pick 34, you?

Answer 54

oh okay. i think i understood. so how to i show my work?

Answer 55

ikd just say it
you already showed it for \(f(11)=34\) there is nothing to compute for the table, it is just given to you

Answer 56

is this okay for the first part?

f(x) = 5x - 21
f(11) = 5 x 11 - 21
f(11) = 55 - 21 = 34.
f(11) = 34.

Answer 57

yes for \(f(11\) sure

Answer 58

is this okay too?

The y-value for 11 is 8. When you compare 34 to 8, 34 is greater in value.

Answer 59

yes

Answer 60

okay, sorry for bothering you. I have one more part left!

Part C: Using the relation in Part B, what is the value of x if f(x) = 99?

Answer 61

solve \[5x-21=99\]for \(x\)

Answer 62

okay

Answer 63

should take two steps only

Answer 64

am i doing it wrong?
5x - 21 = 99
5x - 21 + 5 = 99 + 5
26 + 104 = 130
130 ÷ 5 = 26

Answer 65

x = 26 ??

Answer 66

nope

Answer 67

add 21, divide by 5

Answer 68

where?

Answer 69

\[5x-21=99\] add \(21\) to both sides

Answer 70

so 5x - 21 + 21 = 99 +21
42 + 120 = 162
162 ÷ 5 = 32.4
I don't think thats right.

Answer 71

no it is not

Answer 72

the answer should be 24. but i don't know how to get that

Answer 73

x is not a number, it is variable
you do not find it until the end

Answer 74

\[5x - 21 + 21 = 99 +21 \] is right

Answer 75

but the next step should be \[5x=120\]

Answer 76

then divide by 5

Answer 77

ok.thanks

Answer 78

thank you so much for your help!!. I very much appreciate it.

Answer 79

you helped a lot!