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

Question

. Which inequality shows the range of his earnings given the real-world constraints?(1 point)
Responses

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 f left parenthesis w right parenthesis less than 1,050

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 find the appropriate inequality that shows the range of Dorian's earnings from walking dogs, we need to consider the constraints:

1. He cannot earn negative money, so his earnings must be greater than or equal to zero: \(f(w) \geq 0\).
2. The total earnings are also constrained by a maximum, which in this example will be \(1,050\) based on the implication that he may have a limit to the number of dog walks he can do.

Based on these constraints, the correct inequality that describes the range of his earnings is:

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

Thus, the final answer is:

0≤f(w)≤1,050
(0 less-than-or-equal to f left parenthesis w right parenthesis less-than-or-equal to 1,050)