What Is The Domain Of The Given Function?$\[ \{(3,-2),(6,1),(-1,4),(5,9),(-4,0)\} \\]A. \[$\{x \mid X=-4,-1,3,5,6\}\$\]B. \[$\{y \mid Y=-2,0,1,4,9\}\$\]C. \[$\{x \mid X=-4,-2,-1,0,1,3,4,5,6,9\}\$\]D. \[$\{y \mid
Understanding the Domain of a Function
The domain of a function is the set of all possible input values (x-values) for which the function is defined. In other words, it is the set of all possible x-values that the function can accept without resulting in an undefined or imaginary output. The domain of a function can be a set of numbers, a range of numbers, or even a set of complex numbers.
Identifying the Domain of a Function
To identify the domain of a function, we need to look at the given function and determine the values of x that make the function defined. In the case of the given function, we are given a set of ordered pairs:
Analyzing the Given Function
Looking at the given function, we can see that it is a set of ordered pairs. Each ordered pair consists of an x-value and a corresponding y-value. To determine the domain of the function, we need to look at the x-values in each ordered pair.
Determining the Domain
The x-values in each ordered pair are:
- 3
- 6
- -1
- 5
- -4
These x-values are the only values that the function can accept without resulting in an undefined or imaginary output. Therefore, the domain of the function is the set of all these x-values.
Conclusion
Based on the analysis of the given function, we can conclude that the domain of the function is the set of all x-values that make the function defined. In this case, the domain of the function is:
This is option A.
Why Not Option B?
Option B suggests that the domain of the function is the set of all y-values. However, this is not correct because the domain of a function is the set of all x-values, not y-values.
Why Not Option C?
Option C suggests that the domain of the function is the set of all x-values, including negative numbers and zero. However, this is not correct because the domain of a function is the set of all x-values that make the function defined, not all possible x-values.
Why Not Option D?
Option D suggests that the domain of the function is the set of all y-values, including negative numbers and zero. However, this is not correct because the domain of a function is the set of all x-values, not y-values.
Final Answer
Q: What is the domain of a function?
A: The domain of a function is the set of all possible input values (x-values) for which the function is defined.
Q: How do I determine the domain of a function?
A: To determine the domain of a function, you need to look at the given function and determine the values of x that make the function defined. You can do this by looking at the x-values in each ordered pair.
Q: What is the difference between the domain and the range of a function?
A: The domain of a function is the set of all possible input values (x-values) for which the function is defined, while the range of a function is the set of all possible output values (y-values) that the function can produce.
Q: Can the domain of a function be a set of complex numbers?
A: Yes, the domain of a function can be a set of complex numbers. For example, the function f(z) = z^2 has a domain of all complex numbers.
Q: Can the domain of a function be a set of real numbers?
A: Yes, the domain of a function can be a set of real numbers. For example, the function f(x) = x^2 has a domain of all real numbers.
Q: Can the domain of a function be a set of integers?
A: Yes, the domain of a function can be a set of integers. For example, the function f(x) = x^2 has a domain of all integers.
Q: Can the domain of a function be a set of rational numbers?
A: Yes, the domain of a function can be a set of rational numbers. For example, the function f(x) = x^2 has a domain of all rational numbers.
Q: Can the domain of a function be a set of irrational numbers?
A: Yes, the domain of a function can be a set of irrational numbers. For example, the function f(x) = x^2 has a domain of all irrational numbers.
Q: How do I determine the domain of a function with a square root?
A: To determine the domain of a function with a square root, you need to make sure that the expression inside the square root is non-negative. For example, the function f(x) = √(x^2) has a domain of all non-negative real numbers.
Q: How do I determine the domain of a function with a fraction?
A: To determine the domain of a function with a fraction, you need to make sure that the denominator is not equal to zero. For example, the function f(x) = 1/x has a domain of all real numbers except zero.
Q: How do I determine the domain of a function with a logarithm?
A: To determine the domain of a function with a logarithm, you need to make sure that the expression inside the logarithm is positive. For example, the function f(x) = log(x) has a domain of all positive real numbers.
Q: Can the domain of a function be a set of intervals?
A: Yes, the domain of a function can be a set of intervals. For example, the function f(x) = x^2 has a domain of all real numbers, which can be written as the interval (-∞, ∞).
Q: Can the domain of a function be a set of unions?
A: Yes, the domain of a function can be a set of unions. For example, the function f(x) = x^2 has a domain of all real numbers, which can be written as the union of two intervals: (-∞, 0) and (0, ∞).
Q: Can the domain of a function be a set of intersections?
A: Yes, the domain of a function can be a set of intersections. For example, the function f(x) = x^2 has a domain of all real numbers, which can be written as the intersection of two intervals: (-∞, 0) and (0, ∞).
Q: Can the domain of a function be a set of empty sets?
A: No, the domain of a function cannot be a set of empty sets. The domain of a function must be a non-empty set.
Q: Can the domain of a function be a set of singletons?
A: Yes, the domain of a function can be a set of singletons. For example, the function f(x) = x^2 has a domain of all real numbers, which can be written as the set of singletons {x}.
Q: Can the domain of a function be a set of finite sets?
A: Yes, the domain of a function can be a set of finite sets. For example, the function f(x) = x^2 has a domain of all real numbers, which can be written as the set of finite sets {x1, x2, ..., xn}.
Q: Can the domain of a function be a set of infinite sets?
A: Yes, the domain of a function can be a set of infinite sets. For example, the function f(x) = x^2 has a domain of all real numbers, which can be written as the set of infinite sets {x1, x2, ..., xn, ...}.