U3.L2.HW: Domain and Range: Question 28

Question

Round your answers to two decimal places as needed.

The cost to fill your motor home's propane tank is determined by the function C (g) = 2.89g where C is the output (cost in $) and g is the input (gallons of gas). The propane tank can hold a maximum of 19 gallons.

What is the practical domain of this function?

Minimum Gallons Purchased ≤ g ≤ Maximum Gallons Purchased

Practical Domain: ____________ ≤ g ≤ _____________

What is the practical range of this function?

Minimum Cost ≤ C(g) ≤ Maximum Cost

Practical Range: ___________ ≤ C(g) ≤ _____________

Answer 1

The domain is the possible amount of propane you can put in the tank. Can you put in negative 5 gallons, how about negative 1 gallon? No to these, right? Can you put in zero? I guess so, but that's not too useful. You can also put in one drop, or one gallon, or even 5 gallons (after all it is a 19 gallon tank). So, to write the possible amounts, you use an inequality. 0 < g < 19. This says you can put in anywhere from zero up to 19. To write it, put the smallest number first, then a less than or equal to sign, then the variable, then a second less than or equal to sign, then the largest possible value.

The range is the possible cost when you put in those gallons of propane. It would be 0 < C(g) < 54.91 that is, when you put in zero gallons, it costs zero dollars. When you put in 19 gallons, it costs $54.91

Answer 2

Hi Manny. This is very similar to the problem that I posted a response to earlier. I'd like to try to guide you to finding the right answer,

The practical domain means the possible number of gallons of propane that can be put in the tank. Think about what the fewest possible gallons could be - for instance, could it be a negative number? Also, look carefully at the question to find a clue for the maximum possible value.

The practical range is the range of possible costs. Since our function C(x) is a line and increasing as x gets bigger to find the practical range you should figure out how much it would cost to fill the smallest possible number of gallons and the cost to fill the largest number of possible gallons. That will give you the answer to the practical range.

Post what you think the answer is and I'll be happy to circle back and see if you are on the right track!