Question

lucy makes some extra money working as a referee at youth soccer games. she earns $30 for each game she referees. the function d(g) represents the total amount lucy earns, in dollars, for refereeing g soccer games. what is the range of d(g)? all multiples of 30 less than or equal to 300 all multiples of 30 greater than or equal to 0 all whole numbers from 0 to 30 all real numbers from 0 to 30

Explanation:

Step1: Define the earnings function

The total earnings function is $D(g) = 30g$, where $g$ is the number of games refereed. Since $g$ represents a count of games, $g$ must be a non-negative whole number ($g = 0, 1, 2, 3,...$).

Step2: Identify possible output values

Substitute valid $g$ values into the function:

• When $g=0$, $D(0)=30\times0=0$
• When $g=1$, $D(1)=30\times1=30$
• When $g=2$, $D(2)=30\times2=60$
• And so on.

This means $D(g)$ can only be non-negative multiples of 30.

Step3: Evaluate the options

• "all multiples of 30 less than or equal to 300": There is no stated limit of 300 games, so this is incorrect.
• "all whole numbers from 0 to 30": These are not the earnings amounts, this is incorrect.
• "all real numbers from 0 to 30": $g$ cannot be a non-whole number (you can't referee a fraction of a game), so earnings can't be any real number in this range, this is incorrect.

Answer:

all multiples of 30 greater than or equal to 0