Domain and range of function f(x) = 25x + 100 modelling cost

[tjm]

I'm very confused on my pre-algebra homework over domain and functions. I would be thankful for any help.
Here are the 2 problems and the paragraph that comes before them

The cost of renting a jet-ski at a lake is represented by the equation f(x) = 25x + 100 where x is the number of hours and f(x) is the cost including an hourly rate and a deposit. Choose the letter for the best answer.

What is the domain of the function?
A. x<0 c. x>25
B. x>0 D. x<100

What is the range of the function?
F. f(x) >0 H. f(x)<25
G. f(x)<0 J. f(x) >100

What does this mean? How do I do it? What is the answer?
Thanks in advance!

 

[Deleted member 4993]

Re: Domain and function problems

I'm very confused on my pre-algebra homework over domain and functions. I would be thankful for any help.
Here are the 2 problems and the paragraph that comes before them

The cost of renting a jet-ski at a lake is represented by the equation f(x) = 25x + 100 where x is the number of hours and f(x) is the cost including an hourly rate and a deposit. Choose the letter for the best answer.

What is the domain of the function?
A. x<0 c. x>25
B. x>0 D. x<100



What is the range of the function?
F. f(x) >0 H. f(x)<25
G. f(x)<0 J. f(x) >100

What does this mean? How do I do it? What is the answer?
Thanks in advance!

What are the definitions of range and domain of a function?

If your text-book and class-notes are of no-help, do a google search - and tell us what you found.

 

[tjm]

Re: Domain and function problems

domain - the set of all imput values of a function
range - the set of all possible output of a function

I know the definitions, but I'm still confused .

 

[mmm4444bot]

Re: Domain and function problems

domain - the set of all imput values of a function ...

(Well, here I go again with definitions ...)

For the function named f in the first exercise, I would set in place a conditional definition for its domain.

Domain of f: all values of x for which the number f(x) makes sense. (Here I mean "common" sense, not mathematical sense.)

Does such a conditional definition for the domain of this function help you to understand why x less than zero is one of the incorrect choices?

Think about what the variable symbol x represents; then look at the remaining three choices, and decide which one represents a domain that includes all of the possibilities for x that make sense.

Show me your answer for the domain AND explain why you think so, and then I will help you with the range.

Cheers,

~ Mark

 

[tjm]

Re: Domain and function problems

I think the domain answer must be B. x>0 because the number must be 1 or more to make sense in that situation because it's all positive.

 

[mmm4444bot]

Re: Domain and function problems

I think the domain answer must be B. x>0 because the number must be 1 or more to make sense in that situation because it's all positive.

I agree with the green part, but I do not agree with the red part.

I could rent the jet-ski for 15 minutes.

x = 0.25

That's less than 1.

So, you are correct to say that x must be positive (x>0) because that's what makes sense when talking about an interval of time representing how long you rent something.

Now think about what happens to the number f(x) when x is a positive value. Choose the range that makes sense based on the fact that you know this number is always $100 more than the product of $25 times elapsed hours (x).

Cheers,

~ Mark