Question

1. fuel a car can travel 32 mi for each gallon of gasoline. the function d(x)=32x represents the distance d(x), in miles, that the car can travel with x gallons of gasoline. the cars fuel tank holds 17 gal.
2. nutrition there are 98 international units (ius) of vitamin d in 1 cup of milk. the function v(c)=98c represents the amount v(c) of vitamin d, in ius, you get from c cups of milk. you have a 16 - cup jug of milk.

find a reasonable domain and range for each function. then graph the function.

Explanation:

Problem 22

Step1: Determine domain

The amount of gasoline $x$ in the fuel - tank cannot be negative, and the tank holds 17 gal. So the domain is $0\leq x\leq17$.

Step2: Determine range

When $x = 0$, $d(0)=32\times0 = 0$. When $x = 17$, $d(17)=32\times17=544$. So the range is $0\leq d(x)\leq544$.

Step1: Determine domain

The number of cups $c$ of milk cannot be negative, and you have a 16 - cup jug. So the domain is $0\leq c\leq16$.

Step2: Determine range

When $c = 0$, $V(0)=98\times0 = 0$. When $c = 16$, $V(16)=98\times16 = 1568$. So the range is $0\leq V(c)\leq1568$.

Answer:

Domain: $0\leq x\leq17$; Range: $0\leq d(x)\leq544$

Problem 23