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 \( f(x)=5000+2000 x \), 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 Answer attempt 1 out of 2 in their household would get \( \$ \square \), meaning a qualifying applicant with \( \square \) in the context of the

The function \( f(x) = 5000 + 2000x \) represents the financial aid amount \( f(x) \) that an applicant can receive based on the number of siblings \( x \) they have living in their household. ### Interpretation of the Function Values 1. **Base Financial Aid**: The constant term \( 5000 \) indicates that every qualifying applicant will receive a minimum of \$5000 in financial aid, regardless of the number of siblings. 2. **Additional Aid per Sibling**: The term \( 2000x \) indicates that for each sibling living in the household, the applicant will receive an additional \$2000. ### Example Calculations - If an applicant has **0 siblings**: \[ f(0) = 5000 + 2000(0) = 5000 \] The applicant would receive \$5000. - If an applicant has **1 sibling**: \[ f(1) = 5000 + 2000(1) = 5000 + 2000 = 7000 \] The applicant would receive \$7000. - If an applicant has **2 siblings**: \[ f(2) = 5000 + 2000(2) = 5000 + 4000 = 9000 \] The applicant would receive \$9000. ### Domain of the Function The variable \( x \) represents the number of siblings. Since the number of siblings cannot be negative, the appropriate domain for the function is: \[ x \geq 0 \] In interval notation, this can be expressed as: \[ [0, \infty) \] ### Summary - The function \( f(x) = 5000 + 2000x \) calculates the financial aid based on the number of siblings. - The minimum aid is \$5000, and it increases by \$2000 for each sibling. - The domain of the function is \( [0, \infty) \), meaning \( x \) can take any non-negative integer value.