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

−∞<f(w)≤1,050
negative infinity less than f left parenthesis w right parenthesis less-than-or-equal-to 1,050

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

0≤f(w)<∞

Answer 1

To determine the appropriate inequality that shows the range of Dorian's earnings from walking dogs, we need to consider both the minimum and maximum constraints.

1. **Minimum Earnings**: Dorian cannot earn negative money from walking dogs. So, the minimum earnings are $0. Thus, we have \( f(w) \geq 0 \).

2. **Maximum Earnings**: We need to know how many dogs he can walk to determine the upper limit of his earnings. If we assume that the maximum he can earn is $1,050, we set up \( f(w) \leq 1,050 \).

Putting these together, we can write the range of his earnings as \( 0 \leq f(w) \leq 1,050 \).

Thus, the correct inequality that shows the range of Dorian's earnings is:

**0 ≤ f(w) ≤ 1,050**.