Question

if a function f(m) models the number of hours it take to hike m miles through the jungle, which describes the appropriate domain for the function? a all integers m, where m > 0 b all integers m, where m ≥ 0 c all rational numbers m, where m > 0 d all rational numbers m, where m ≥ 0

Explanation:

1. First, understand the domain of a function representing miles hiked. Miles can be a non - negative rational number (e.g., 0 miles means not hiking, 2.5 miles is a valid distance).

• Integers are too restrictive because distance can be a fraction (like 1.5 miles). So options A and B (which use integers) are incorrect.
• The distance hiked can be 0 miles (when you haven't started hiking yet), so \(m\geq0\). Option C has \(m > 0\) which would exclude the case of 0 miles, so it's incorrect.
• Option D says all rational numbers \(m\) where \(m\geq0\), which is correct because miles can be 0 (no hiking) or a positive rational number (like 1, 1.2, 3/2 etc.).

Answer:

D. all rational numbers m, where \(m\geq0\)