What Is The Range Of The Function For The Given Domain?$\[ \begin{array}{l} y = 2x - 5 \\ D: \{-2, 0, 2, 4\} \end{array} \\]Select The Correct Answer.A. \[$ R: \{-9, 0, -1, 3\} \$\]B. \[$ R: \{9, -5, 9, 13\} \$\]C. \[$ R:
When dealing with functions, it's essential to understand the relationship between the domain and the range. The domain refers to the set of input values for which the function is defined, while the range represents the set of possible output values. In this article, we'll explore how to determine the range of a function for a given domain.
What is the Range of a Function?
The range of a function is the set of all possible output values it can produce for the given input values in the domain. In other words, it's the set of all possible y-values that the function can take for the given x-values in the domain.
Given Function and Domain
The given function is y = 2x - 5, and the domain is D = {-2, 0, 2, 4}. To find the range, we need to substitute each value in the domain into the function and calculate the corresponding output value.
Calculating the Range
Let's substitute each value in the domain into the function and calculate the corresponding output value.
- For x = -2, y = 2(-2) - 5 = -9
- For x = 0, y = 2(0) - 5 = -5
- For x = 2, y = 2(2) - 5 = -1
- For x = 4, y = 2(4) - 5 = 3
Determining the Range
Based on the calculations above, the possible output values for the given domain are -9, -5, -1, and 3. Therefore, the range of the function for the given domain is R = {-9, -5, -1, 3}.
Conclusion
In conclusion, the range of a function for a given domain can be determined by substituting each value in the domain into the function and calculating the corresponding output value. By understanding the relationship between the domain and the range, we can better analyze and interpret the behavior of functions.
Answer
In the previous article, we explored how to determine the range of a function for a given domain. In this article, we'll answer some frequently asked questions related to this topic.
Q: What is the difference between the domain and the range of a function?
A: The domain of a function refers to the set of input values for which the function is defined, while the range represents the set of possible output values. In other words, the domain is the set of all possible x-values, and the range is the set of all possible y-values.
Q: How do I determine the range of a function for a given domain?
A: To determine the range of a function for a given domain, you need to substitute each value in the domain into the function and calculate the corresponding output value. This will give you the set of all possible output values, which is the range of the function.
Q: What if the function is not defined for all values in the domain?
A: If the function is not defined for all values in the domain, you need to identify the values for which the function is not defined and exclude them from the domain. Then, you can proceed to determine the range of the function for the remaining values in the domain.
Q: Can the range of a function be empty?
A: Yes, the range of a function can be empty. This occurs when the function is not defined for any value in the domain, or when the function always produces the same output value.
Q: How do I know if the range of a function is finite or infinite?
A: To determine if the range of a function is finite or infinite, you need to analyze the behavior of the function as the input values approach positive or negative infinity. If the function approaches a finite value as the input values approach infinity, the range is finite. Otherwise, the range is infinite.
Q: Can the range of a function be a single value?
A: Yes, the range of a function can be a single value. This occurs when the function is a constant function, meaning that it always produces the same output value.
Q: How do I graph the range of a function?
A: To graph the range of a function, you need to plot the set of all possible output values on a coordinate plane. This will give you a visual representation of the range of the function.
Q: Can the range of a function be a set of intervals?
A: Yes, the range of a function can be a set of intervals. This occurs when the function produces different output values for different input values.
Conclusion
In conclusion, understanding the range of a function for a given domain is an essential concept in mathematics. By answering these frequently asked questions, we hope to have provided a better understanding of this topic and how to apply it in different situations.
Additional Resources
For more information on the range of a function, we recommend the following resources:
- Khan Academy: Range of a Function
- Math Is Fun: Range of a Function
- Wolfram MathWorld: Range of a Function
We hope this article has been helpful in answering your questions about the range of a function for a given domain. If you have any further questions or need additional clarification, please don't hesitate to ask.