Question

d $p(x) = 6.39x - 7570$ because the number of hot dogs sold changes
key: ✓ student response correct answer

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:

The problem involves linear functions. To determine the correct function, we analyze the slope and y - intercept. The function in option A, \(f(x)=\frac{18}{5}x + 41\), and the recursive function in option D, \(f(n)=f(n - 1)+\frac{18}{5};f(0)=41\), are consistent. The slope \(\frac{18}{5}\) (or the common difference in the recursive formula) and the initial value (y - intercept or \(f(0)\)) of 41 match the characteristics of a linear function. The other options have incorrect y - intercepts (option B has 184, option C has a different slope and y - intercept) or incorrect slopes.

Answer:

A. \(f(x)=\frac{18}{5}x + 41\)
D. \(f(n)=f(n - 1)+\frac{18}{5};f(0)=41\)