Limits and Continuity of Cost Function for Mailing Letters: Domain and Graph

[iRaid]

Homework Statement

Postal charges are $.25 for the first ounce and $.20 for each additional ounce or fraction thereof. Let c be the cost function for mailing a letter weighing w ounces.
a) Is c a continuous function? What is the domain?
b) What is c(1.9)? c(2.01)? c(2.89)?
c) Graph the function c.

Homework Equations

The Attempt at a Solution

For a I got:
No. The domain is all real numbers > 0.
B is where I get stuck, I understand the question it's just I can't get what the integer function would be..
C I could do once I have b..

 

[SammyS]

Can you answer B simply by applying what is stated, without resorting to some sort of mathematical "formula" ?

 

[iRaid]

I guess I can answer b, but then how would I graph the function for part c :|

edit: I see what you are getting it, I think I can make a graph too, thanks lol :p

 

[iRaid]

Well I got the answers, but for my own knowledge can you tell me what this function would actually be?

 

[SammyS]

Are you referring to the Greatest Integer function when you say "the integer function" ?

There are many integer functions. Two common ones are the "floor" function (a.k.a. Greatest Integer function), and the "ceiling" function.

 

[iRaid]

Yep ment greatest integer function, I'm pretty sure it's applied here since it says: $.20 for each additional ounce or fraction thereof

 

[SammyS]

Greatest Integer function, a.k.a. floor function

floor(x) = the greatest integer that's less than or equal to x .

Doesn't work: floor(1.9) = 1

floor(x) + 1 is close, floor(1.9) + 1 = 2 ---- but floor(1) + 1 = 2, not 1 .
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Try -floor(-x):

-floor(-(1.9)) = - (-2) = 2 , OK

-floor(-(1)) = - (-1) = 1 , OK
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