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Answer :
To solve this question, we need to determine the type of numbers most reasonable for the domain of the function [tex]\( c = 3.75x \)[/tex], where [tex]\( x \)[/tex] is the number of letters in a monogramming project.
1. Understanding the Context:
- The company charges based on the number of letters in the project.
- [tex]\( x \)[/tex] represents the number of letters, so it must be a countable quantity.
2. Analyzing the Options:
- a. All integers: Integers include both positive and negative whole numbers, as well as zero. However, you can't have a negative number of letters or even zero letters for a project, as each project must include at least one letter.
- b. All whole numbers: Whole numbers are non-negative integers (0, 1, 2, 3, ...). While zero is included in whole numbers, logically, a project would consist of at least one letter. Hence, all whole numbers except zero would be reasonable.
- c. All real numbers: This includes all rational and irrational numbers, which also encompasses fractions and decimals. A fractional or decimal number of letters doesn't make practical sense in this context, as you can't have part of a letter.
- d. All of the above: This option means the domain could be any of the previously mentioned numbers, which we've seen is not reasonable for the context.
3. Conclusion:
- The most reasonable domain for the number of letters [tex]\( x \)[/tex] is all whole numbers, specifically starting from 1 onward, since you can't have a project with zero or negative letters.
Therefore, the most reasonable type of number for the domain of this situation is b. All whole numbers.
1. Understanding the Context:
- The company charges based on the number of letters in the project.
- [tex]\( x \)[/tex] represents the number of letters, so it must be a countable quantity.
2. Analyzing the Options:
- a. All integers: Integers include both positive and negative whole numbers, as well as zero. However, you can't have a negative number of letters or even zero letters for a project, as each project must include at least one letter.
- b. All whole numbers: Whole numbers are non-negative integers (0, 1, 2, 3, ...). While zero is included in whole numbers, logically, a project would consist of at least one letter. Hence, all whole numbers except zero would be reasonable.
- c. All real numbers: This includes all rational and irrational numbers, which also encompasses fractions and decimals. A fractional or decimal number of letters doesn't make practical sense in this context, as you can't have part of a letter.
- d. All of the above: This option means the domain could be any of the previously mentioned numbers, which we've seen is not reasonable for the context.
3. Conclusion:
- The most reasonable domain for the number of letters [tex]\( x \)[/tex] is all whole numbers, specifically starting from 1 onward, since you can't have a project with zero or negative letters.
Therefore, the most reasonable type of number for the domain of this situation is b. All whole numbers.
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