Questions: For the function involving the variables listed, use your intuition or additional research, if necessary, to complete parts (a) through (c) below. (altitude, temperature) when climbing a mountain a. Describe an appropriate domain and range for the function. Choose the appropriate domain for the function below. A. The domain is all altitudes of interest or 0 ft to 15,000 ft. B. The domain is all temperatures corresponding to altitudes of interest or 0°F to 90°F. C. The domain is all temperatures corresponding to altitudes of interest or 70°F to 90°F. D. The domain is all altitudes of interest or 0 ft to 50,000 ft.

Solution Steps

To determine an appropriate domain and range for the function involving altitude and temperature when climbing a mountain, consider the realistic altitudes and temperatures one might encounter. The domain should reflect the range of altitudes that are typically of interest when climbing a mountain, and the range should reflect the corresponding temperatures at those altitudes.

To establish an appropriate domain for the function involving altitude and temperature when climbing a mountain, we consider realistic altitudes. The options provided are:

• A: \(0 \, \text{ft} \) to \(15,000 \, \text{ft}\)
• B: \(0^{\circ} \text{F} \) to \(90^{\circ} \text{F}\)
• C: \(70^{\circ} \text{F} \) to \(90^{\circ} \text{F}\)
• D: \(0 \, \text{ft} \) to \(50,000 \, \text{ft}\)

Among these, option A, which specifies the domain as \(0 \, \text{ft} \) to \(15,000 \, \text{ft}\), is the most appropriate for typical mountain climbing scenarios.

Based on the analysis of the options, the appropriate domain for the function is determined to be \(0 \, \text{ft} \) to \(15,000 \, \text{ft}\).

Final Answer