Question

a
$f(x)=\frac{18}{5}x + 41$
b
$f(x)=\frac{18}{5}x + 184$
c
$f(x)=\frac{5}{18}x + 58$
d
$f(n)=f(n - 1)+\frac{18}{5}; f(0)=41$
key: student response

Explanation:

To determine the correct function, we analyze the options. Option A, \( f(x)=\frac{18}{5}x + 41 \), and Option D, \( f(n)=f(n - 1)+\frac{18}{5}; f(0)=41 \), are related as the recursive formula in D defines an arithmetic sequence with common difference \( \frac{18}{5} \) and initial term 41, which corresponds to the linear function in A (since a linear function \( y=mx + b \) can be represented recursively with slope \( m \) as the common difference and \( b \) as the initial term when \( x = 0 \)). Options B and C have incorrect y - intercepts or slopes. The student's selection of A is correct as it matches the recursive definition in D (if we consider the context of linear functions and recursive sequences) and has the correct slope and y - intercept.

Answer:

A. \( f(x)=\frac{18}{5}x + 41 \)