Question

if the function f(y) = n models the number, n, of inches a tree grows in a year, y, which describes an appropriate domain for the function? a all integers where y > 0 b all integers where y ≥ 0 c all rational numbers where y > 0 d all rational numbers where y ≥ 0

Explanation:

1. First, understand the variable \( y \): \( y \) represents the number of years a tree grows. Years can be non - negative (including zero, but in the context of a tree's growth, \( y = 0 \) might represent the initial time, and we can have fractions of a year in theory, so \( y \) should be a rational number (since we can measure time in parts of a year like half - a - year).
2. Analyze the domain: The number of years \( y \) cannot be negative. So \( y\geq0 \). Also, time can be represented as a rational number (e.g., 1.5 years is a valid time for a tree to grow). Integers would be too restrictive because we can have non - integer values for the number of years (for example, if we are measuring the growth over a period of 6 months, \( y = 0.5 \)). So the domain should be all rational numbers where \( y\geq0 \).

Answer:

D. all rational numbers where \( y \geq 0 \)