The air temperature decreases about \( 5^{\circ} \mathrm{F} \) for each increase of 1,000 feet in altitude. If the outside temperature at ground level in a certain location is \( 68^{\circ} \mathrm{F} \), then the air temperature \( y \) is represented by the function \( y=-5 x+68 \), where \( x \) is the altitude (in thousands of feet). Which of the following sets of numbers would be appropriate input values for the given situation? Select all that apply. A) integers B) only zero C) whole numbers D) positive numbers E) rational numbers F) negative numbers

To determine the appropriate input values for the function \( y = -5x + 68 \), where \( x \) represents the altitude in thousands of feet, we need to consider the context of the problem. 1. **Understanding the variable \( x \)**: - \( x \) represents altitude in thousands of feet. Therefore, \( x \) can take values starting from \( 0 \) (ground level) and increasing as altitude increases. 2. **Analyzing the options**: - **A) integers**: This includes negative numbers, which are not applicable since altitude cannot be negative. Therefore, this option is not appropriate. - **B) only zero**: This is too restrictive since \( x \) can take values greater than zero as well. Thus, this option is not appropriate. - **C) whole numbers**: This includes \( 0, 1, 2, \ldots \) which are valid inputs for altitude. Therefore, this option is appropriate. - **D) positive numbers**: This includes all numbers greater than zero, which are valid inputs for altitude. Therefore, this option is appropriate. - **E) rational numbers**: This includes all fractions and whole numbers. Since altitude can be expressed in fractions of thousands of feet (e.g., \( 0.5 \) for 500 feet), this option is appropriate. - **F) negative numbers**: This is not appropriate since altitude cannot be negative. 3. **Conclusion**: The appropriate input values for the given situation are: - C) whole numbers - D) positive numbers - E) rational numbers Thus, the final answer is C, D, and E.