SOLUTION: Okay, so I am doing my algebra homework, and my teacher was gone today so he wasn't here to explain what we do. Could you possibly help me solve this: "Your car holds 16 gallons o

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Question 897962: Okay, so I am doing my algebra homework, and my teacher was gone today so he wasn't here to explain what we do. Could you possibly help me solve this:
"Your car holds 16 gallons of gas. What would be the reasonable domain and range for the cost to fill up your tank if gas costs $3 per gallon?"
It'd be very much appreciated if you help! I would have tried to solve it, but I don't even know where to begin. Please and thank you very much!
Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Let

x = number of gallons
y = cost to fill up the tank (with x gallons of gas)

x is just a number, which is unknown. Say x = 1. This means that it costs 3*1 = 3 dollars to fill up the tank. So we have the pair x = 1, y = 3. This represents the point (1,3) on the graph. This visually tells you the cost when x = 1 or tells you how many gallons you get for $3.

when x = 2, y = 3*2 = 6
when x = 3, y = 3*3 = 9
when x = 4, y = 3*4 = 12
etc etc

In general, we have this equation y = 3x

That equation tells you to take any gallon amount (x) and multiply it by 3 to get the total cost (y). This is assuming the $3 amount includes taxes and other surcharges.

----------------------------------------------------------------------------

The domain is the set of allowed inputs for x. So this means the domain is the set of nonnegative numbers that are less than or equal to 16. We cannot have a negative number of gallons, so that's why x is nonnegative. Furthermore, we can't fill up the tank past 16 gallons, which explains the "less than or equal to 16"

Algebraically, the domain is . This says: x is between 0 and 16 including both endpoints.

In interval notation, the domain is [0,16]. The square brackets tell us to include the endpoints.

----------------------------------------------------------------------------
The smallest number in the domain is x = 0

Plug this into the equation y = 3x

y = 3x

y = 3*0

y = 0

So the smallest number in the range is y = 0. Makes sense because if you don't fill your tank, then it costs you $0, ie nothing.

The largest number in the domain is x = 16. This is the most we can fill up the tank.

y = 3x

y = 3*16 ... replace x with 16

y = 48


So if we go to the max of the domain (x = 16) we go to the max of the range (y = 48). In the real world, if we fill up the tank completely and buy 16 gallons of gas, we spend $48.

So the range is

In interval notation, the range is [0,48]. Again, the square brackets tell us to include the endpoints.
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
Let x = the number of gallons in your tank when you arrive
at the filling station:

Let y = the cost to fill your tank.

If your tank is empty, then x = 0 and y = $16×3 = $48

If your tank is already full then x = 16 and you will not need
any gas and it will cost you nothing, so y = $0

So the graph will be a line from the point (0,$48) to (16,$0)

So the domain will be 0 ≦ x ≦ 16 and the range will be 0 ≦ y ≦ 48

In interval notation the domain is [0,16] and the range is [0,$48]

The graph will look like this



Edwin
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