dont fall asleep on me math geniuses

going to be semi easy intermediate college algebra questions

ok:

let g(x) = 3/5x +4

is (-5,2) on the graph of the function?
if x=-15, what is g(x)
if g(x)=-2, what is x

thats first question, must show work - 25 fg winner

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a company offers long distance calls that charges $7 per month plus 5 cents per minute.

a) find linear function that expresses the month long-distance cost c(x) as a function of the minutes x.

b ) what is the domain of this linear function

c) what is the cost if a person made 215 minutes worth of long-distance calls during one month

d) in one, how many mins of long distance can be purchased for $32.00

this is last question probably, must show work - 50 fg winner

ps- its not that i cant do these, but dont have time

thanks

This post was edited by KINGSTANNIS on Feb 7 2016 11:30pm

no longer need last question did myself

This post was edited by KINGSTANNIS on Feb 8 2016 12:26am

g(x) = 3/5*x + 4

Is (-5, 2) on this line? NO. Check by plugging in -5 for x.
g(-5) = 3/5*(-5) + 4
g(-5) = -3 + 4
g(-5) = 1..... (-5, 1) is on the line

If x = -15, what is g(x)? Again get this answer simply by plugging -15 in for x
g(-15) = 3/5*(-15) + 4
g(-15) = -9 + 4
g(-15) = -5

If g(x) = -2, what is x? This is obtained by plugging -2 in for g(x) on the left side and solving for x.
-2 = 3/5*x + 4
-6 = 3/5*x
-10 = x
You can check this back by plugging -10 in for x in the original equation.

a ) A company offers long distance calls at $7 per month plus 5 cent per minute. Hence, no matter how little you call a month, you will still need to pay the 7 dollars. It is therefore independent of x. We want to find a function c(x) describing the cost of calling x minutes a month. We know that the cost each month is dependent of how many minutes we call per month, where the cost of calling 1 min is 5 c.

Hence the cost is: c(x) = 7+(1/20)x.

Where 1/20 is because we have different units. The cost independent of x is in dollars, and the other in cents. 5 cents is 1/20 of a dollar.

b ) The domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined, in this case x.

The function is defined for every real number which is greater than or equal to zero (real as we can call for instance 1.2 minutes, and greater or equal to 0 as we can call 0 minutes a month, but we can never call LESS than 0 minute

Hm.. this one may be a bit tricky depending on what your tutor is after. If the tutor means the domain of the function IN PRACTICE, then the domain would be [0,44 640] (0 I've already described why, 44 640 as it is the total amount of minutes in a month if it is a 31 day month, i.e. 31 days * 24 hours a day * 60 minutes an hour = 44 640.

On the other hand, if the deal also means that this is connected to several phones, which can be used by people at the same time, then [0,infinity) (never use ] at infinity, as it is not a number).

If the tutor refers to the function ITSELF, then (-infinity, infinity) because there are no points on the function where it is not continuos. oO

E: I would assume they are after [0,44 640] as I guess that answer has the most "understanding" of the problem and to practically interpret math questions, without complicating things with several people being able to use different phones etc. In previous examples/assignments of this nature, what have the tutor/book refered to when taking the domain of practical questions?

c ) c(125) = 7 +(1/20)*125 = $13.25

d ) We solve for:
7+(1/20)*x = 32 <==>
(1/20)*x = 25 <==>
x= 25*20 <==>
x = 500

Hence for $32 we can call 500 minutes.

(Note if you wish you can write (1/20) as 0.05 if that is what you prefer)

This post was edited by Cenderze on Feb 8 2016 06:01pm