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?

- anonymous

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- anonymous

- anonymous

i do not know.

- anonymous

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## More answers

- jim_thompson5910

The range is the set of possible outputs. So it's saying that the set of possible outputs are
-13, -8, -3, 12, 17

- anonymous

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

- jim_thompson5910

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

- jim_thompson5910

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

- anonymous

oh now i get it thanks!!! :D

- jim_thompson5910

you're welcome

- anonymous

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

- anonymous

- jim_thompson5910

let me check

- jim_thompson5910

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

- anonymous

okay let me try it again

- anonymous

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

- jim_thompson5910

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

- anonymous

yeah but i dont undersand it that much

- jim_thompson5910

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?

- anonymous

-1 ?

- anonymous

i mean -4

- jim_thompson5910

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

- jim_thompson5910

I'll be right back

- anonymous

okay

- jim_thompson5910

I'm back

- jim_thompson5910

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

- anonymous

yes

- jim_thompson5910

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

- anonymous

2?

- jim_thompson5910

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

- anonymous

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

- jim_thompson5910

I can't help with tests

- anonymous

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

- anonymous

- jim_thompson5910

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

- anonymous

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.

- anonymous

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

- jim_thompson5910

ok let me look through it

- anonymous

okay

- jim_thompson5910

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

- anonymous

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

- jim_thompson5910

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

- jim_thompson5910

let me find a calculator

- anonymous

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

- jim_thompson5910

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

- anonymous

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

- jim_thompson5910

I got that as well

- jim_thompson5910

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

- anonymous

thas what i dont get because it a big division

- jim_thompson5910

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

- jim_thompson5910

So this means it costs $24 to make 6 widgets

- anonymous

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

- anonymous

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

- jim_thompson5910

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

- jim_thompson5910

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

- anonymous

and how you know which ones where on the same parentesis

- jim_thompson5910

what do you mean?

- anonymous

some of the numbers where in the same parenthesis

- anonymous

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

- anonymous

- jim_thompson5910

alright I'm glad it's making sense now

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