Royston's car had 15 1/5 gallons of gas at the start of the trip. During the trip, he stopped at a gas station and he refueled the car with 5 3/5 gallons. If the car consumed 17 4/5 gallons of gas during the trip, there are still ____________ gallons of gas remaining in the tank?

Y is less than or equal to 5.

Final answer:

The range of the absolute value function f(x) = 5 - |x - 4| is (-∞ , 5] because the function will always be less than or equal to 5, but there's no lower limit as the function will decrease indefinitely as |x - 4| increases.

Explanation:

The function given is f(x) = 5 - |x - 4|, which represents an absolute value function. The range of a function refers to the possible values of f(x) or y in the function. In general, the absolute value function has a range of all non-negative numbers. However, because the function is subtracted from 5, the values of this particular function will decrease as x moves away from 4, in either direction.

Therefore, the maximum value of the function occurs when the absolute value equals to zero (i.e., x = 4), then f(x) = 5 - 0 = 5. As you move away from 4, the absolute value increases and thus subtracts more from 5, making f(x) smaller. So, f(x) will always be less than or equal to 5, but there is no lower limit, as the function will continue to decrease indefinitely as |x - 4| increases. Hence the range of the function f(x) = 5 - |x - 4| is (-∞ , 5].

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