Question

If the range of the function f(x)= 5x − 3 is {-13, -8, -3, 12, 17}, what is its domain?
I am confused with the 5x-3, can someone help?

Answer 1

@iCake @ICanAwnserQuestions

Answer 2

i do not know.

Answer 3

@jim_thompson5910

Answer 4

The range is the set of possible outputs. So it's saying that the set of possible outputs are

-13, -8, -3, 12, 17

Answer 5

yeah i get that what i dont get is the 5x-3

Answer 6

it wants the corresponding inputs for each output

so say the output is y = -13

that means

y = 5x - 3
-13 = 5x - 3
-13+3 = 5x
-10 = 5x
5x = -10
x = -10/5
x = -2

So if the output is y = -13, then the input is x = -2

Answer 7

you will do this for the other outputs to get the domain

Answer 8

oh now i get it thanks!!! :D

Answer 9

you're welcome

Answer 10

what did you get? i get -2,-1,0,1,2

Answer 11

@jim_thompson5910

Answer 12

let me check

Answer 13

I don't agree with 1 or 2
but the "-2,-1,0" part is correct

Answer 14

okay let me try it again

Answer 15

i dont get it what i have to do with the y=-13 and x-2 @jim_thompson5910

Answer 16

do you see how I plugged in y = -13 and solved to get x = -2 ?

Answer 17

yeah but i dont undersand it that much

Answer 18

well the idea is that if you plug in x =-2, you'll get y = -13 out

they want you to think in reverse. If y = -8 is the output, then what must the input be?

Answer 19

-1 ?

Answer 20

i mean -4

Answer 21

yep because

y = 5x-3
y = 5*(-1) - 3 ... replace x with -1
y = -5 - 3
y = -8

so this shows how if x = -1 is plugged in, then y = -8 pops out

Answer 22

I'll be right back

Answer 23

okay

Answer 24

I'm back

Answer 25

So do you see how plugging in x = -1 gives y = -8?

Answer 26

yes

Answer 27

and if y = -3, then what must x be?

Answer 28

2?

Answer 29

let's check

y = 5x-3
y = 5*2 - 3 ... replace x with 2
y = 10-3
y = 7

so if x = 2, then y = 7
but we want y = -3

Answer 30

i get it! thank you! I have 4 questions more can you help me? its for a home test

Answer 31

I can't help with tests

Answer 32

its practically a homework and its the last 4 questions that i have trouble with :/

Answer 33

@jim_thompson5910

Answer 34

Ok I'll help with 2 of them if it's a hw. Which 2 are giving you the most trouble?

Answer 35

widget wonder produce widgets. They have found that the cost,c(x), of making x widgets is a quadratic function in terms of x.


The company also discovered that it cost $16 to produce 2 widgets, $18 to produce 4 widgets, and $48 to produce 10 widgets.

Find the total cost of producing 6 widgets.

Answer 36

i am so bad at that kind of problems like the paraghrap @jim_thompson5910

Answer 37

ok let me look through it

Answer 38

okay

Answer 39

do you have a TI calculator (like a TI83 or TI84) ?

Answer 40

no :/ but cellphone work? or a scientific calculator?

Answer 41

the cellphone won't work because we need to do quadratic interpolation

Answer 42

let me find a calculator

Answer 43

okay thanks for your effort and your time ;) :D

Answer 44

ok I found this page

http://www.solvemymath.com/online_math_calculator/interpolation.php

you will type in [2,16], [4,18], [10,48] and hit calculate. Tell me what comes up

Answer 45

it appear this: http://solvemymath.com/calc_data/draw_data/cache/be7017ac8ee524153679ac985295e596.png

Answer 46

I got that as well

Answer 47

now you plug x = 6 into that function to get your final answer

Answer 48

thas what i dont get because it a big division

Answer 49

\[\Large f(x) = \frac{x^2-4x+36}{2}\]
\[\Large f(6) = \frac{6^2-4(6)+36}{2}\]
\[\Large f(6) = \frac{36-4(6)+36}{2}\]
\[\Large f(6) = \frac{36-24+36}{2}\]
\[\Large f(6) = \frac{12+36}{2}\]
\[\Large f(6) = \frac{48}{2}\]
\[\Large f(6) = 24\]

Answer 50

So this means it costs $24 to make 6 widgets

Answer 51

ohh okay so i always going to subsitute the x for its value

Answer 52

and how do you get that list of numbers? like this one that you type [2,16], [4,18], [10,48] @jim_thompson5910

Answer 53

Given: "The company also discovered that it cost $16 to produce 2 widgets, $18 to produce 4 widgets, and $48 to produce 10 widgets."


"it cost $16 to produce 2 widgets" means x = 2 and y = 16
"$18 to produce 4 widgets" means x = 4 and y = 18
"$48 to produce 10 widgets" means x = 10 and y = 48

Answer 54

all that means we know (2,16), (4, 18) and (10,48) all lie on this parabola

Answer 55

and how you know which ones where on the same parentesis

Answer 56

what do you mean?

Answer 57

some of the numbers where in the same parenthesis

Answer 58

oh nevermind i get it. thanks for your help! i have to go Thanks a lot!!

Answer 59

@jim_thompson5910

Answer 60

alright I'm glad it's making sense now