HELP
Lian's truck has a
25 gallon tank and uses 0.05 gallon of gas
for every mile driven. When creating a table
for the function y = -0.05x + 25, Lian
argues that he can only use positive
rational numbers for the input. Is Lian
correct? Justify your answer.
Well, Lian's argument seems a bit tanked! Using only positive rational numbers for the input in this case is not necessary. You see, the function y = -0.05x + 25 represents Lian's truck's gas consumption.
Since the number of miles driven, x, can be any non-negative rational number (including fractions or decimals), there's no need to limit it to positive rational numbers only. Lian can also input zero miles to see how much gas is left in the tank without driving anywhere—a pretty easy pancake-like situation!
So, Lian doesn't need to worry. Whether he's driving a little or not at all, his function will still work just fine.
To determine whether Lian is correct in arguing that he can only use positive rational numbers for the input, let's analyze the equation y = -0.05x + 25.
First, let's consider the term -0.05x. This term represents the amount of gas used for every mile driven (0.05 gallon per mile). It is multiplied by the input value "x" which represents the number of miles driven.
Since "x" represents the number of miles driven, it is reasonable to assume that "x" can take any non-negative value, including positive rational numbers.
Next, let's consider the constant term 25. This represents the initial amount of gas in Lian's truck tank, given that the tank has a 25-gallon capacity.
Since the initial amount of gas in the tank is a fixed quantity, it is not influenced by the value of "x". It remains the same regardless of the input, so it does not restrict Lian to specific values for "x".
Based on this analysis, Lian's argument is not correct. He can use not only positive rational numbers but also non-negative rational numbers (including zero) as inputs for the function y = -0.05x + 25.
To determine if Lian can only use positive rational numbers as input for the function y = -0.05x + 25, we need to understand what the function represents.
In this case, the function represents the relationship between the number of miles driven (x) and the amount of gas left in Lian's truck (y). The equation -0.05x + 25 shows how the amount of gas left in the truck decreases as the number of miles driven increases.
Now, let's consider Lian's argument that he can only use positive rational numbers as input. Positive rational numbers are numbers that can be expressed as a fraction, with both the numerator and denominator being positive integers.
In the context of Lian's truck, the input (number of miles driven, x) can be any non-negative real number. This means that x can be positive or zero. It can also be a rational number, an irrational number, or a decimal value.
For example, if Lian wants to calculate the amount of gas left after driving 10 miles, he can plug the value 10 into the equation y = -0.05x + 25. The result will be a valid output.
Therefore, Lian's argument that he can only use positive rational numbers for the input is incorrect. The input for this function can be any non-negative real number, including rational and irrational numbers.