Answer :
Final Answer:
The given function \( f(x) = 5000 + 1000x \) represents the financial aid available based on the number of siblings an applicant has, with $5000 being the initial aid and $1000 added per sibling.
Explanation:
The provided function \( f(x) = 5000 + 1000x \) depicts the financial aid an applicant can receive based on the count of siblings in their household. The term \( 5000 \) stands for the base financial aid provided regardless of the number of siblings. For each additional sibling (inclusive of half siblings and step siblings), an extra \( 1000 \) dollars is added to the initial aid, thus increasing the total aid available to the applicant.
Interpreting the function, \( x \) represents the number of siblings an applicant has. For instance, if an applicant has \( 2 \) siblings, the total financial aid they can receive will be \( f(2) = 5000 + 1000 \times 2 = 7000 \) dollars. This means the base aid of $5000 is augmented by $2000 ($1000 per sibling), leading to a total of $7000.
Domain: The domain of the function \( f(x) = 5000 + 1000x \) is determined by the number of siblings, which should be a non-negative integer (including zero). Since the number of siblings cannot be negative and generally are counted in whole numbers, the domain of this function would be all non-negative integers.
The interpretation of mathematical functions in real-world scenarios, especially in finance or economics, often involves understanding the relationship between variables and outcomes. Analyzing functions like these helps in making informed decisions regarding financial planning and assistance programs.
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Full Question:
"A college has a financial aid formula that applies to applicants whose family's income is below a certain threshold. The financial aid can be determined by the function f(x)=5000+1000x, where x is the number of siblings (including half siblings and step siblings) that the applicant has living in their household. Find and interpret the given function values and determine an appropriate domain for the function.
