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, left bracket, x, right bracket, equals, 20000, plus, 5000, x, commaf(x)=20000+5000x, where xx 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

f, left bracket, minus, 2, right bracket, equalsf(−2)=
, meaning a qualifying applicant with
siblings in their household would get $
in financial aid. This interpretation
in the context of the problem.
f, left bracket, 4, right bracket, equalsf(4)=
, meaning a qualifying applicant with
siblings in their household would get $
in financial aid. This interpretation
in the context of the problem.
f, left bracket, 3, point, 5, right bracket, equalsf(3.5)=
, meaning a qualifying applicant with
siblings in their household would get $
in financial aid. This interpretation
in the context of the problem.
Based on the observations above, it is clear that an appropriate domain for the function is
.

Answer 1

1) A qualifying applicant with -2 siblings would $10,000 in financial aid.

This interpretation is not practical since the number of siblings cannot be negative

2) A qualifying applicant with 4 siblings would get $40,000 in financial aid.

3) A qualifying applicant with 3.5 siblings would get $37,500 in financial aid.

This interpretation is also questionable as the number of siblings is typically a whole number.

4) Domain is positive integers.

How the financial aid was calculated.

Given that : (x)=20000+5000x

where

x is number of siblings

f(x) is financial aid

Let's evaluate the given function values:

1) When x = -2

f(-2) = 20000 + 5000(-2)

= 20000 - 10000 = 10000

Interpretation: A qualifying applicant with -2 siblings would get $10,000 in financial aid. This interpretation doesn't make practical sense since the number of siblings can't be negative.

2) When x = 4

f(4) = 20000 + 5000(4)

= 20000 + 20000 = 40000

Interpretation: A qualifying applicant with 4 siblings would get $40,000 in financial aid.

3) For f(3.5) = 20000 + 5000(3.5)

= 20000 + 17500

= 37500

Interpretation: A qualifying applicant with 3.5 siblings would get $37,500 in financial aid. This interpretation is also questionable as the number of siblings is typically a whole number.

Based on these observations, an appropriate domain for the function should be limited to non-negative integers since it's not realistic to have a negative or fractional number of siblings. Therefore, the appropriate domain is x belonging to the set of non-negative integers. In mathematical notation: (x ε 0, 1, 2, 3, ...}).