Question

for the function involving the variables listed, use your intuition or additional research, if necessary, to complete parts (a) through (c) below.

(price of gasoline, number of tourists in a national park)

a. describe an appropriate domain and range for the function.

choose the appropriate domain for the function below.

a. the domain is all realistic gasoline prices or \\$0.25 per gallon to \\$1.50 per gallon
b. the domain is all realistic gasoline prices or \\$2 per gallon to \\$4 per gallon
c. the domain is the numbers of tourists visiting the park or 2500 people to 15,000 people.
d. the domain is the numbers of tourists visiting the park or 0 people to 1 million people.

Explanation:

Identify independent and dependent variables

Using the Independent and Dependent Variables knowledge point

• Independent variable (input): price of gasoline (typically drives economic behavior, such as travel choices).
• Dependent variable (output): number of tourists in a national park (depends on travel costs like gasoline prices).

Determine the domain of the function

Using the Domain and Range knowledge point

• The domain consists of all possible input values (independent variable), which is the price of gasoline.
• Realistic gasoline prices are represented by a range such as \$2 per gallon to \$4 per gallon, rather than extremely low historical prices like \$0.25 to \$1.50.
• Therefore, the correct option is (B).

Answer:

• (A) The domain is all realistic gasoline prices or $0.25 per gallon to $1.50 per gallon
• (B) The domain is all realistic gasoline prices or $2 per gallon to $4 per gallon (Correct answer)
• (C) The domain is the numbers of tourists visiting the park or 2500 people to 15,000 people
• (D) The domain is the numbers of tourists visiting the park or 0 people to 1 million people