Select all representations for the domain of a function given by elevation (in feet) at or above sea level.(2 points)
Responses
(−∞, ∞
)
(−∞, ∞
)
{x|x≥0}
start set x such that x is greater than or equal to 0 end set
{x|x∈R}
start set x such that x is in the real numbers end set
{x|x>0}
start set x such that x is greater than 0 end set
(0, ∞)
(0, ∞)
[0, ∞)
{x|x≥0} and [0, ∞)
The correct representations for the domain of a function given by elevation (in feet) at or above sea level are:
- {x|x≥0} (start set x such that x is greater than or equal to 0 end set)
- {x|x∈R} (start set x such that x is in the real numbers end set)
- [0, ∞)
To determine the representations for the domain of a function given by elevation at or above sea level, we need to consider the restrictions on the values of the independent variable (usually denoted as x) that are meaningful for the function.
1. (−∞, ∞)
This represents the entire real number line, including all negative and positive numbers. It implies that there are no restrictions on the domain, meaning any value of x is allowed.
2. {x|x≥0}
This represents the set of all real numbers x such that x is greater than or equal to 0. It means that the function is defined for values of x that are either equal to or greater than 0.
3. {x|x∈R}
This represents the set of all real numbers x. It implies that any real number can be the input for the function.
4. {x|x>0}
This represents the set of all real numbers x such that x is greater than 0. It means that the function is defined for values of x that are strictly greater than 0.
5. (0, ∞)
This represents the interval from 0 to positive infinity, excluding 0. It implies that the function is defined for values of x that are greater than 0, but not including 0.
6. [0, ∞)
This represents the interval from 0 to positive infinity, including 0. It means that the function is defined for values of x that are greater than or equal to 0.
Therefore, the correct representations for the domain of the function given by elevation at or above sea level are:
- (−∞, ∞)
- {x|x≥0}
- {x|x∈R}
- {x|x>0}
- (0, ∞)
- [0, ∞)