Question

a gaming store rents out video game consoles for $75 per day. the consoles can be rented for either 1 day, 3 days or 7 days. the cost in dollars to rent a console is a function of the number of days it is rented.
what is the domain and range of the part of the linear function shown?
which answer choices best describe the domain and range of the function for this situation?
select two correct answers.
domain: 0 ≤ x ≤ 6
domain: 4,000 ≤ x ≤ 7,500
domain: 0 ≤ g(x) ≤ 6
range: 0 ≤ g(x) ≤ 7,500
range: 4,000 ≤ g(x) ≤ 7,500
the variable used to represent range is (y) which means the total amount of tickets sold. the range for this situation is: y: {0,2,4,6,8,10}
the variable used to represent domain is (x) which means the number of tickets. the domain for this situation is: x: {0,1,2,3,4,5}
water (gallons)
volume of pool water
time (hours)

Explanation:

Step1: Identify domain and range for water - time graph

The x - axis represents time (in hours) and ranges from 0 to 6. So the domain is \(0\leq x\leq6\). The y - axis represents volume of pool water (in gallons) and ranges from 0 to 9000. But the visible part of the graph shows values from 0 to 8000. So a reasonable range for the shown part is \(0\leq g(x)\leq8000\) (assuming \(g(x)\) represents the volume function with respect to time \(x\)).

Step2: Analyze console - rental problem

The console can be rented for 1, 3, or 7 days. So the domain (number of days) is \(\{1,3,7\}\). The cost \(y\) of renting is \(y = 75x\) where \(x\) is the number of days. When \(x = 1\), \(y=75\); when \(x = 3\), \(y = 225\); when \(x = 7\), \(y=525\). So the range is \(\{75,225,525\}\).

Step3: Analyze ticket - amount problem

The x - variable represents the number of tickets and is \(\{0,1,2,3,4,5\}\). The y - variable represents the total amount. If we assume a linear relationship (not given explicitly but from the graph shape), we can see the corresponding y - values. The range for the y - values (total amount) based on the points on the graph is \(\{0,2,4,6,8\}\).

Answer:

For the water - time graph: Domain: \(0\leq x\leq6\), Range: \(0\leq g(x)\leq8000\)
For the console - rental: Domain: \(\{1,3,7\}\), Range: \(\{75,225,525\}\)
For the ticket - amount: Domain: \(\{0,1,2,3,4,5\}\), Range: \(\{0,2,4,6,8\}\)