Domain and Range of a function problem help

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Bogogogo

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I understand how to find x of a function and how they work, and have gotten the first two problems correct. However I am struggling in finding the Domain and Range of the problem. I have forgotten how to find the do,Ian and range, but remember there being a formula-like solution method. Could someone please help me through this problem?

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In an applied problem like this, the domain is determined not primarily by the expression you've written (which is probably the "formula-like" method you have in mind), but by the meaning of the variables. If x is the length of a side, it has to be positive. In addition, the expressions you will have written for each other side must also be positive. Those inequalities determine what values x may have.

The range is in general trickier; but in this case, it will be determined by your answer to the unstated problem of maximizing the volume. The volume can't be greater than the maximum you find (and it also has to be positive).

What are the hints they give?
 
The hint for the first one is "The domain of f is the set of values the input quantity can assume. What values can the cutout length (in inches) assume?"

And the second; The range of f is the set of values the output quantity can assume. What values can the volume of the box (in cubic inches) assume?
 
Dr.Peterson said:
In an applied problem like this, the domain is determined not primarily by the expression you've written (which is probably the "formula-like" method you have in mind), but by the meaning of the variables. If x is the length of a side, it has to be positive. In addition, the expressions you will have written for each other side must also be positive. Those inequalities determine what values x may have.

The range is in general trickier; but in this case, it will be determined by your answer to the unstated problem of maximizing the volume. The volume can't be greater than the maximum you find (and it also has to be positive).

What are the hints they give?
Click to expand...
Sorry I pressed the wrong reply button,

The hint for the first one is "The domain of f is the set of values the input quantity can assume. What values can the cutout length (in inches) assume?"

And the second; The range of f is the set of values the output quantity can assume. What values can the volume of the box (in cubic inches) assume?
 
Bogogogo said:
Sorry I pressed the wrong reply button,

The hint for the first one is "The domain of f is the set of values the input quantity can assume. What values can the cutout length (in inches) assume?"

And the second; The range of f is the set of values the output quantity can assume. What values can the volume of the box (in cubic inches) assume?
Click to expand...
Dr. P already expanded on the hint you were given. This is a problem in physics. So physical constraints limit x.

Can x be non-positive? Obviously not.

Now translate that into mathematical language.

[MATH]0.< x.[/MATH]
Can 5 - 2x be non-negative? Obviously not. So?

The range problem is harder. I'd solve it with calculus, but presumably you have been taught an algebraic method.
 
I think both hints are meant to lead to the ideas I mentioned. I thought they might explicitly mention finding the maximum volume, but it is implied.

I presume you have learned how to find that maximum.
 
Solve x>0 AND (5-2x)>0 AND (7-2x)>0
x>0 AND x<5/2 AND x<7/2
So what can x be?
 
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