Select all representations for the domain of a function given by elevation (in feet) at or above sea level.
Responses:
(0, ∞)
(−∞, ∞ )
[0, ∞)
{x|x∈R}
{x|x>0}
{x|x≥0}
(0, ∞)
[0, ∞)
{x|x>0}
{x|x≥0}
The correct representations for the domain of a function given by elevation (in feet) at or above sea level are:
1. [0, ∞) - This represents all non-negative real numbers, including 0.
2. {x|x≥0} - This represents all real numbers greater than or equal to 0.
Therefore, the correct responses are: [0, ∞) and {x|x≥0}.
To determine the representations for the domain of a function given by elevation at or above sea level, we need to understand what the domain represents in this specific context.
The domain of a function refers to the set of all possible values for the independent variable, which is usually denoted as "x." In the case of elevation at or above sea level, the independent variable could be the height or the distance from sea level.
Now, let's go through each representation and see if it accurately describes the domain of the function:
(0, ∞): This represents all positive numbers greater than zero. It means that the elevation cannot be zero or negative. This would be an appropriate representation for the domain.
(-∞, ∞): This represents all real numbers. In the context of elevation, this would include negative values as well, which do not make sense since we are discussing elevations at or above sea level. This representation is not appropriate for the domain.
[0, ∞): This represents all non-negative numbers, including zero and positive numbers. Since the function is defined to be at or above sea level, this representation includes all valid values. This would be an appropriate representation for the domain.
{x|x∈R}: This represents all the real numbers. Similar to the second representation, this includes negative values that are not relevant in this context. This representation is not appropriate for the domain.
{x|x>0}: This represents all values greater than zero, excluding zero itself. Since the function is defined to be at or above sea level, this would exclude sea level itself, which is not correct. This representation is not appropriate for the domain.
{x|x≥0}: This represents all non-negative numbers, including zero and positive numbers. This is similar to the third representation, [0, ∞), and it correctly includes all valid values for the domain.
Therefore, the appropriate representations for the domain of the function given by elevation at or above sea level are:
(0, ∞)
[0, ∞)
{x|x≥0}