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How would you use domain and range to determine whether a relation is a function?
Each element in the domain must be mapped to one and only one element in the range. If that condition is satisfied then the mapping (or relationship) is a function. Different elements in the domain can be mapped to the same element in the range. Some elements in the range may not have any elements from the domain mapped to them. These do not matter for the mapping to be a function. They do matter in terms of the function having an inverse, but that is an entirely different matter. As an illustration, consider the mapping from the domain [-10, 10] to the range [-10, 100] with the mapping defined by y = x2.
Is the relation a function Why or why not (3 1) (3 0) (3 4) (3 8)?
No it is not. The number 3, in the domain, gets mapped to more than one number in the range.
Why the graph of a function never has 2 different points with the same x- coordinate because?
It is because a function is defined as a relation which cannot be one-to-many.
What is a relation in which each element of the first set is paired with exactly one element of the second set?
If every element of the first set is paired with exactly one element of the second set, it is called an injective (or one-to-one) function.An example of such a relation is below.Let f(x) and x be the set R (the set of all real numbers)f(x)= x3, clearly this maps every element of the first set, x, to one and only one element of the second set, f(x), even though every element of the second set is not mapped to.
Can an invertible function have more than one x-intercept?
No. If the function has more than one x-intercept then there are more than one values of x for which y = 0. This means that, for the inverse function, y = 0 should be mapped onto more than one x values. That is, the inverse function would be many-to-one. But a function cannot be many-to-one. So the "inverse" is not a function. And tat means the original function is not invertible.
What makes a relation a function?
A relation is a mapping from one set to another. It is a function if elements of the first set are mapped to only one element from the second set. So, for example, square root is not a function because 9 can be mapped to -3 and 3.
Which relation are function relation?
A relation is a mapping between two sets, a domain and a range. A function is a relationship which allocates, to each element of the domain, exactly one element of the range although several elements of the domain may be mapped to the same element in the range.
What is the relation in which each element in the domain is mapped to exactly one element the range?
It is an invertible function.
How do you determined if a relation is a function?
For every element on the domain, the relationship must allocate a unique element in the codomain (range). Many elements in the domain can be mapped to the same element in the codomain but not the other way around. Such a relationship is a function.
How would you use domain and range to determine whether a relation is a function?
Each element in the domain must be mapped to one and only one element in the range. If that condition is satisfied then the mapping (or relationship) is a function. Different elements in the domain can be mapped to the same element in the range. Some elements in the range may not have any elements from the domain mapped to them. These do not matter for the mapping to be a function. They do matter in terms of the function having an inverse, but that is an entirely different matter. As an illustration, consider the mapping from the domain [-10, 10] to the range [-10, 100] with the mapping defined by y = x2.
A relation in which each element in the domain is mapped to exactly one element inthe range?
It is an injective relation.
Name a function where each domain element is mapped to the same range element?
The constant function is an example where each domain element is mapped to the same range element. This function always outputs the same value regardless of the input.
How do you find if a relation is a function?
A relationship is a function if every element in the domain is mapped onto only one element in the codomain (range). In graph terms, it means that any line parallel to the vertical axis can meet the graph in at most one point.
How does the domain relate to a function?
Any function is a mapping from a domain to a codomain or range. Each element of the domain is mapped on to a unique element in the range by the function.
How do you identify a function?
A function is a mapping from one set to another such that each element from the first set is mapped onto exactly one element from the second set.
What relations are function in math?
A function is a mapping from one set to another such that each element of the first set (the domain) is mapped to one element of the second set (the range).
Why it is valid to say that both a function and its inverse describe the same relationship.?
If a function has an inverse then it is a bijection between two sets. Each element in the first set is mapped to one, and only one, element of the second set. Therefore, for each element in the second set there is one, and only one, element in the first set. The function and its inverse, both define the relationship between the same pairs of elements.
