Questions: Linear Functions Quick Check 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) 0 ≤ f(w)<∞ -∞<f(w) ≤ 1,050 0<f(w)<1,050 0 ≤ f(w) ≤ 1,050

Solution Steps

We are given a linear function \( f(w) = 15w \) that models the total amount of money Dorian earns by walking dogs, where \( w \) is the number of dogs walked. We need to determine the range of his earnings given real-world constraints.

In the real world, Dorian cannot earn a negative amount of money, so the minimum value of \( f(w) \) is 0. Additionally, if there is a maximum number of dogs he can walk, this would limit his earnings. The problem suggests a maximum earning of \$1,050.

The range of the function \( f(w) = 15w \) is determined by the possible values of \( w \). Since \( w \) must be a non-negative integer (as he cannot walk a negative number of dogs), the minimum value of \( f(w) \) is 0. The maximum value, given the constraint, is \$1,050.

Given the constraints, the range of Dorian's earnings is from 0 to \$1,050, inclusive. Therefore, the correct inequality is:

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

Final Answer