I need some help please. Write a function rule to describe each statement...
the cost in dollars of printing dollar bills when it costs 3.8cents to print a dollar bill.
the amount of money you earn mowing lawns at $15 per lawn.
the profit you make selling flowers at $1.50 each when each flower costs you $.80

- anonymous

- katieb

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- anonymous

it costs 3.8 cents to print 1 dollar
its costs 2 times 3.8 cents to print two dollars
it costs 3 times 3.8 cents to print 3 dollars
you can see a pattern here right?

- anonymous

yeah,but how do i write them as function rules?

- anonymous

we use variables!
there should be two of them; one will represent the number of dollars, lets call that x and the other will represent the cost to print them, lets call that y

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## More answers

- anonymous

my teacher told me to write the functions as f(x)=...

- anonymous

ok lets use f(x) instead of y
so the cost to print, f(x), should equal the number of dollars, x, times 3.8 cents

- anonymous

so f(x)=3.8x

- anonymous

yes

- anonymous

ok so then for the second one would it be... f(x)=$15x

- anonymous

yep

- anonymous

but actually I made a mistake on the first one

- anonymous

I d dont understand how to write the third one though.

- anonymous

the function for the first part should give us the cost in dollars, with f(x) = 3.8x we'll end up with the number of cents

- anonymous

so you just convert 3.8 cents into dollars which should be .038

- anonymous

the profit you make selling flowers at $1.50 each when each flower costs you $.80

- anonymous

what is the profit if I sell one flower?

- anonymous

70 cents

- anonymous

right..
and if i sell two flowers?

- anonymous

a dollar and 40 cents

- anonymous

which is the same as 2 times 70 cents right?
if I sell 3 flowers the profit would be 3 times 70 cents
and if I sell x flowers the profit will be x times 70 cents

- anonymous

ok so... would the function be f(x)=.70x?

- anonymous

yes! good job

- anonymous

Thanks. Now i have another question i have this equation... f(x)=$0.59x where x+number of pounds. if i had $10 to buy that turkey how big a turkey could i buy?

- anonymous

you have f(x) = $0.59x which in words is, the cost of a turkey, f(x), is the number of pounds, x, times 59 cents

- anonymous

so the cost of a turkey is a function of the number of pounds that it weighs, does that make sense so far?

- anonymous

yeah. i was wondering where you d plug in the $10.

- anonymous

the ten dollars goes where dollars is represented in the equation

- anonymous

x is pounds
f(x) is dollars
so the equation, when we put in 10 dollars, becomes
$10 = $0.59x

- anonymous

and by solving for x you will have found out how big a turkey you could by with 10 dollars

- anonymous

does that make sense?

- anonymous

16.95lb. is what i got. Yeah it does make sense.

- anonymous

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- anonymous

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- anonymous

i dont see the rule for either of these. It says to write a function rule. By the way.. they are two seperate questions.

- anonymous

ok lets start with the top one
we need to find a way to relate x and y
in other words we need to be able to describe how much y changes when x changes
we can do this with a function
y = x times (some number)

- anonymous

i know that,but idk what number it should be.,

- anonymous

we can find out what number it is by calculating the slope between the points that are given

- anonymous

with m = (y2-y1)/(x2-x1)

- anonymous

ok. so what should i get?

- anonymous

lets use the points: (0,1) and (1,3)
m = (3-1)/(1-0) = 2

- anonymous

i understand it for the second table the answer would be f(x)=-4.5x. But i still dont see a pattern in the first one.

- anonymous

maybe graphing the points and seeing them line up would help

- anonymous

the y's are going up by two except for the last one.

- anonymous

because its a negative x in the last one, if it were positive 3 then y would be 7

- anonymous

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- anonymous

thats the pattern if we follow the negative x points

- anonymous

the reason it isnt as easy to see as the second problem is because this function will have the form y = mx + b

- anonymous

whereas the second one was just y = mx

- anonymous

ok so whats the function rule.

- anonymous

well we're using y = mx + b as the template for our function, we found m to be 2, now we need to find b

- anonymous

so we have y = 2x + b
since we're given points we can substitute one in for the values of x and y, and then solve for b
so if we use (0,1) as our point we get
1 = 2(0) + b
so b = -1

- anonymous

and keep in mind that we could have used any of the points that were given
for example if we used (2,5) we get
5 = 2(2) +b
and again b = -1

- anonymous

so now that we know b, we can finally write the function as
y = 2x -1

- anonymous

thank you.

- anonymous

np :)

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