maval engineer uses the function, P, to analyze the effects of water pressure on submarines. Th
ction P(d) measures the pressure exerted by water, where d represents the depth of water in
ters. Which of the following would be a possible domain?
d is the set of all integers.
d is the set of all integers where d > 0
d is the set of all rational numbers.
d is the set of all rational numbers where (0 ≤ d ≤ depth of sea floor
The possible domain for the function P(d) would be d is the set of all rational numbers where (0 ≤ d ≤ depth of sea floor).
Explain
The domain of a function refers to the set of all possible input values for the function. In this case, the function P(d) measures the pressure exerted by water, where d represents the depth of water in meters.
Since depth is typically measured as a positive value, we can eliminate the option where d is the set of all integers, as this would include negative values.
The option where d is the set of all integers where d > 0 is a valid possibility. However, it is more restrictive than necessary, as it only allows for positive integers to be used as input.
The option where d is the set of all rational numbers is also a possibility, as rational numbers include both positive and negative values as well as fractions. However, it is less specific than necessary, as it would allow for depths that may not be physically realistic or within the given context.
The most appropriate option is the one where d is the set of all rational numbers where (0 ≤ d ≤ depth of sea floor). This option ensures that the input values for the function are positive and within a specific range that corresponds to the depth of the sea floor. It provides a more realistic and relevant domain for the function.