A function is created to represent the height above sea level of a mountain climber every hour. What restrictions would be made to the range?
A-range includes all real numbers
B-range includes positive integers
C-range includes positive real numbers
D-range includes negitive real numbers
I think it is B. I am not sure though.
Thanks!
The correct answer is C. The range includes positive real numbers.
Since the function represents the height above sea level, the values can be any positive real number, as the climber can ascend to any height above sea level. Therefore, the range of the function would include positive real numbers.
To determine the answer, we need to consider the given information about the function and the context of the problem.
The function represents the height above sea level of a mountain climber every hour. Since height can be measured in decimals, it suggests that the function should be continuous and capable of providing decimal values.
Moreover, the height above sea level can't be negative for the mountain climber, as it is physically impossible to have a negative height. Therefore, negative real numbers are not part of the range.
Now, let's consider the options:
A) The range includes all real numbers: This option could be true if the function allows negative heights, which is not the case here.
B) The range includes positive integers: This option could be possible if the function only takes integer values for the height above sea level. However, this is unlikely since heights can be measured in decimals.
C) The range includes positive real numbers: This option aligns with the given information. Since the function represents the height above sea level and heights can be decimal values, the range would include positive real numbers.
D) The range includes negative real numbers: As mentioned earlier, negative heights are not possible for a mountain climber, so this option can be ruled out.
Therefore, the correct answer is C) The range includes positive real numbers.
I hope this explanation helps you understand the reasoning behind the correct answer.