I need precalculus help!! (function notation)

Question

A tank has 16 gallons of water in it when water begins draining from the tank. (Recall that water weighs 8.345 pounds per gallon.)

a. If 22 pounds of water have drained from the tank, how many gallons of water are remaining in the tank?

b. Define a function f that determines the number of gallons of water in the tank, f(w), in terms of the number of pounds of water that have drained from the tank since the tank started draining, w.

c. What is the domain of f? Enter your answer as an interval.

d. What is the range of f? Enter your answer as an interval.

Answer 1

16 gallons = 16(8.345) = 133.52 pounds

f(w) = w/8.345 = gallons

maximum pound tank limit = 38(8.345) = 317.11 lb

16 gallons = 16(8.345) = 133.52 lb.

133.52-22 = 111.52 lbs left = 111.52/8.345

= 13.363691 gallons left after 22 pounds drained off from 16 gallons

domain = [0, 38(8.345)]= [0,317.11]

range = [0, 38]

Answer 2

a. First we need to find the number of gallons of water in 22 pounds of water. 

The conversion factor given is 8.345 pounds per gallon:

  8.345 pounds

^{____________________}

  1 gallon

 

Next we multiply this by the 22 pounds of water :

22 pounds ·   1gallon = 2.64 gallons

    ^{__________________}

8.345 pounds

We then subtract this from the 16 gallons to find the amount left in the tank:

16 - 2.88 = 13.36 gallons

b. First we can divide the conversion factor to get a decimal: 

f(w) = 16 - (0.1198w)  

c. This is a linear function and w can be any real number. 

Domain: {-∞, ∞}

Practically speaking the w can only take a positive value since you cannot have a negative weight.

d. The range is also any real number.

Range: {-∞, ∞}

Practically speaking the range for the tank is only from 0 to 16 gallons of water. 

Answer 3