Select all representations for the domain of a function given by elevation (in feet) at or above sea level.(2 points)
Responses
(0, ∞)
(0, ∞)
{x|x≥0}
start set x such that x is greater than or equal to 0 end set
{x|x>0}
start set x such that x is greater than 0 end set
[0, ∞)
[0, ∞)
{x|x∈R}
start set x such that x is in the real numbers end set
(−∞, ∞
)
(0, ∞)
{x|x≥0}
{x|x>0}
[0, ∞)
{x|x∈R}
The correct representations for the domain of a function given by elevation (in feet) at or above sea level are:
- (0, ∞)
- [0, ∞)
- {x | x ≥ 0}
- {x | x > 0}
- {x | x ∈ R}
To select all representations for the domain of a function given by elevation (in feet) at or above sea level, we need to consider the conditions for the domain.
First, we can eliminate options that have a condition where the elevation can be below sea level. Since the function is specifically for elevations at or above sea level, any representation that allows for negative values should be excluded.
On this basis, we can eliminate the following options:
(0, ∞)
(−∞, ∞)
Next, let's review the remaining options:
{ x | x ≥ 0 }
This representation states that x belongs to a set, such that x is greater than or equal to 0. This means that the function's domain includes all real numbers greater than or equal to zero.
{x | x > 0}
This representation states that x belongs to a set, such that x is greater than 0. This means that the function's domain includes all real numbers greater than zero.
[0, ∞)
This representation uses brackets to indicate that both endpoints, 0 and infinity, are included in the domain. This means that the function's domain includes all real numbers greater than or equal to zero.
{ x | x ∈ R }
This representation states that x belongs to a set of real numbers. This means that the function's domain includes all real numbers.
Based on the conditions given, all of the following representations are correct for the domain of the function given by elevation at or above sea level:
{ x | x ≥ 0 }
{x | x > 0}
[0, ∞)
{ x | x ∈ R }