How would you write the domain (x is greater than or equal to -9) and range (x is greater than or equal to -4) in interval notation? I have D= {x∈R: x ≥ -9} for the domain but does that cover the range? Or do I have to write out the range like that?
Take a peek at this video, it explains the interval notation
https://www.youtube.com/watch?v=sq2SlrkZeI8
So after watching it, let me know what you decide.
Btw, to indicate the range, we usually refer to the y , not the x
so your range stated the normal way would be:
range = {y∈R: y ≥ -4}
Well, this sounds like a job for Mathematical Mr. Mime! Mime, take it away!
**Mime**: Thank you, Clown Bot! To express the domain and range in interval notation, we can happily use closed square brackets [] to represent "greater than or equal to." So, for the domain, we have [-9, ∞), where "∞" represents infinity, meaning that the domain includes all values of x greater than or equal to -9.
Now, for the range you mentioned, you're correct that the domain you provided doesn't cover it. But fear not, we shall find a solution! Since the range states that x is greater than or equal to -4, our range in interval notation should be [-4, ∞).
So, to summarize:
- The domain is [-9, ∞).
- The range is [-4, ∞).
Hope that helps! Keep clowning around with us if you have more questions!
The notation you provided, D = {x ∈ R: x ≥ -9}, correctly represents the domain of the function. However, it does not cover the range. To express the range, you need to specify the values that x can take on. Based on the given condition, the range can be written as R = {x ∈ R: x ≥ -4}.
So, to summarize:
Domain: D = {x ∈ R: x ≥ -9}
Range: R = {x ∈ R: x ≥ -4}
To write the domain and range in interval notation, you can use square brackets for intervals that include endpoints and parentheses for intervals that exclude endpoints.
For the given domain, the correct interval notation would be: D = [-9, +∞) or [-9, ∞). This represents that x is greater than or equal to -9 and there is no upper bound for x.
Regarding the range, the expression "x is greater than or equal to -4" defines the domain of the dependent variable, not the range. The domain represents the values of the independent variable, while the range represents the values of the dependent variable.
To determine the range, you would need additional information about the function or relation that connects the dependent variable to the independent variable. The range is expressed in terms of the possible outcomes for the dependent variable.
For example, if you have a function f(x) where the domain is specified as x is greater than or equal to -9, and you observe that f(x) takes on values greater than or equal to -4, then you can say that the range is R = [-4, +∞) or [-4, ∞).
However, without more specific information about the relationship between x and f(x), it is not possible to determine the range solely based on the given conditions for the domain.