Find the domain and range of the relation and determine whether it is a function?
Answers are
Domain x>1 range y>0yes it is a function
Domain all real numbers,range all real numbers yes it is a function
Domain positive integers, range positive integers no it is not a function
Domain x>0, range>1 no it is not a function
Thanks
To determine the domain and range of a relation and determine if it is a function, we need to understand the terms "domain," "range," and "function."
The domain of a relation represents the set of all possible input values, or x-values, for the relation. In other words, it is the set of values that x can take.
The range of a relation represents the set of all possible output values, or y-values, for the relation. In other words, it is the set of values that y can take.
A function is a type of relation where every input value (x) is associated with only one output value (y). In other words, for a relation to be a function, each x-value in the domain should have a unique y-value in the range.
Let's analyze each answer to determine the domain, range, and if it is a function:
Answer 1: Domain x > 1, Range y > 0 - Yes, it is a function.
In this case, the domain consists of all values of x greater than 1. The range consists of all values of y greater than 0. As long as each x-value greater than 1 maps to a unique y-value greater than 0, it is a function.
Answer 2: Domain all real numbers, Range all real numbers - Yes, it is a function.
In this case, the domain consists of all real numbers, and the range also consists of all real numbers. As long as each real number maps to a unique real number, it is a function.
Answer 3: Domain positive integers, Range positive integers - No, it is not a function.
In this case, the domain consists of positive integers, and the range consists of positive integers. However, a function requires a unique y-value for each x-value. If any positive integer in the domain is not matched with a unique positive integer in the range, then it is not a function.
Answer 4: Domain x > 0, Range > 1 - No, it is not a function.
In this case, the domain consists of all values of x greater than 0, and the range consists of all values of y greater than 1. Similar to the previous case, a function requires a unique y-value for each x-value. If any x-value greater than 0 is not matched with a unique y-value greater than 1, then it is not a function.
Based on the analysis, answer 1 and answer 2 describe relations that are functions, while answer 3 and answer 4 do not describe functions.
I hope this explanation helps! Let me know if you have any further questions.
To determine the domain and range of a relation, we need more information about the relation itself. However, I can help explain the given answers and discuss the concept of a function.
1. "Domain x>1, range y>0. Yes, it is a function": This answer states that the domain consists of all values greater than 1, and the range consists of all values greater than 0. It also states that the relation is a function. However, without knowing the explicit relation, it is difficult to confirm if it is indeed a function.
2. "Domain all real numbers, range all real numbers. Yes, it is a function": This answer states that the domain and range include all real numbers. Furthermore, it states that the relation is a function. Similarly, without knowing the specific relation, we cannot determine if it is a function.
3. "Domain positive integers, range positive integers. No, it is not a function": This answer specifies that the domain and range consist of positive integers. Additionally, it claims that the relation is not a function. The reason it is not a function is that a function requires each input (x-value) to have a unique output (y-value). If multiple positive integers have the same output, then the relation does not meet this requirement.
4. "Domain x>0, range y>1. No, it is not a function": This answer describes a domain where x-values are greater than 0 and a range where y-values are greater than 1. It states that the relation is not a function. Similarly to the previous examples, we cannot determine if it is indeed a function without understanding the specific relation.
To fully determine whether a relation is a function, we need to know how each input (x-value) is related to the corresponding output (y-value) in the relation.