Question

Dorian earns $15 every time he walks a dog. He models the total amount of money he makes walking dogs with the equation f(w)=15w . Which inequality shows the range of his earnings given the real-world constraints?(1 point) Responses 0<f(w)<1,050 0 less than f left parenthesis w right parenthesis less than 1,050 0≤f(w)<∞ 0 less-than-or-equal-to f left parenthesis w right parenthesis less than infinity 0≤f(w)≤1,050 0 less-than-or-equal-to f left parenthesis w right parenthesis less-than-or-equal-to 1,050 −∞<f(w)≤1,050

Answer 1

To determine the appropriate inequality showing the range of Dorian's earnings based on the equation \( f(w) = 15w \), we can analyze the situation:

1. Earnings Structure: Dorian earns $15 for each dog he walks, meaning:

   • If he walks 0 dogs, his earnings \( f(0) = 15 \cdot 0 = 0 \).
   • If he walks a certain number \( w \) of dogs, his total earnings are directly proportional to \( w \), and hence they must be non-negative.

2. Upper Bound: Since there is a typical constraint that limits the maximum amount of money he can realistically earn, we can assume that there is a cap on his earnings, such as a maximum of $1,050.

Based on this information, the correct inequality representing the range of his earnings should be:

\[ 0 \leq f(w) \leq 1,050 \]

This indicates that he can earn from $0 (if he walks zero dogs) to a maximum of $1,050. Therefore, the correct response is:

0 ≤ f(w) ≤ 1,050