Select The Correct Answer.Consider Functions \[$ M \$\] And \[$ N \$\].$\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -5 & -3 & -1 & 3 & 5 \\ \hline n(x) & 2 & 1 & -3 & 1.5 & 0 \\ \hline \end{array} \\]What Is The Value Of \[$
Introduction
Functions are a fundamental concept in mathematics, and understanding how to evaluate them is crucial for solving problems in various fields. In this article, we will explore the concept of functions and how to select the correct answer when given a table of values.
What is a Function?
A function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range. It is a way of describing a relationship between two variables, where each input corresponds to exactly one output. In other words, a function takes an input and produces a unique output.
Evaluating Functions
To evaluate a function, we need to find the output value for a given input. This can be done by substituting the input value into the function and simplifying the expression. In the case of a table of values, we can simply look up the output value for a given input.
The Given Table of Values
The following table shows the values of the functions { m $}$ and { n $}$ for different inputs:
| x | -5 | -3 | -1 | 3 | 5 |
|---|---|---|---|---|---|
| n(x) | 2 | 1 | -3 | 1.5 | 0 |
What is the Value of { n(3) $}$?
To find the value of { n(3) $}$, we need to look up the output value for the input x = 3 in the table. According to the table, the value of n(x) for x = 3 is 1.5.
What is the Value of { n(-1) $}$?
To find the value of { n(-1) $}$, we need to look up the output value for the input x = -1 in the table. According to the table, the value of n(x) for x = -1 is -3.
What is the Value of { n(5) $}$?
To find the value of { n(5) $}$, we need to look up the output value for the input x = 5 in the table. According to the table, the value of n(x) for x = 5 is 0.
Conclusion
In conclusion, to select the correct answer when given a table of values, we need to look up the output value for the given input. This can be done by substituting the input value into the function and simplifying the expression, or by simply looking up the output value in the table.
Common Mistakes to Avoid
When evaluating functions, there are several common mistakes to avoid:
- Not checking the domain: Make sure to check the domain of the function to ensure that the input value is within the valid range.
- Not checking the range: Make sure to check the range of the function to ensure that the output value is within the valid range.
- Not using the correct table of values: Make sure to use the correct table of values for the function being evaluated.
- Not looking up the output value: Make sure to look up the output value for the given input in the table.
Final Thoughts
In conclusion, understanding functions and how to evaluate them is crucial for solving problems in various fields. By following the steps outlined in this article, you can select the correct answer when given a table of values. Remember to check the domain and range of the function, use the correct table of values, and look up the output value for the given input.
Additional Resources
Practice Problems
- Evaluate the function f(x) = 2x + 1 for x = 3.
- Evaluate the function g(x) = x^2 - 4 for x = -2.
- Evaluate the function h(x) = x^3 - 2x^2 + x + 1 for x = 2.
Conclusion
Q: What is a function?
A: A function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range. It is a way of describing a relationship between two variables, where each input corresponds to exactly one output.
Q: How do I evaluate a function?
A: To evaluate a function, you need to find the output value for a given input. This can be done by substituting the input value into the function and simplifying the expression. In the case of a table of values, you can simply look up the output value for a given input.
Q: What is the difference between a function and a relation?
A: A function is a relation where each input corresponds to exactly one output. A relation, on the other hand, is a set of ordered pairs where each input may correspond to more than one output.
Q: How do I determine if a relation is a function?
A: To determine if a relation is a function, you need to check if each input corresponds to exactly one output. If each input has a unique output, then the relation is a function.
Q: What is the domain of a function?
A: The domain of a function is the set of all possible input values. It is the set of all x-values for which the function is defined.
Q: What is the range of a function?
A: The range of a function is the set of all possible output values. It is the set of all y-values for which the function is defined.
Q: How do I find the domain and range of a function?
A: To find the domain and range of a function, you need to examine the function and determine the set of all possible input and output values.
Q: What is the difference between a function and an equation?
A: A function is a relation where each input corresponds to exactly one output. An equation, on the other hand, is a statement that two expressions are equal.
Q: How do I determine if an equation is a function?
A: To determine if an equation is a function, you need to check if each input corresponds to exactly one output. If each input has a unique output, then the equation is a function.
Q: What is the value of { n(-5) $}$?
A: According to the table, the value of n(x) for x = -5 is 2.
Q: What is the value of { n(3) $}$?
A: According to the table, the value of n(x) for x = 3 is 1.5.
Q: What is the value of { n(5) $}$?
A: According to the table, the value of n(x) for x = 5 is 0.
Q: How do I evaluate a function with a table of values?
A: To evaluate a function with a table of values, you need to look up the output value for the given input in the table.
Q: What are some common mistakes to avoid when evaluating functions?
A: Some common mistakes to avoid when evaluating functions include:
- Not checking the domain of the function
- Not checking the range of the function
- Not using the correct table of values
- Not looking up the output value for the given input
Q: How do I determine if a function is increasing or decreasing?
A: To determine if a function is increasing or decreasing, you need to examine the function and determine if the output value increases or decreases as the input value increases.
Q: What is the difference between an increasing and a decreasing function?
A: An increasing function is a function where the output value increases as the input value increases. A decreasing function is a function where the output value decreases as the input value increases.
Q: How do I find the inverse of a function?
A: To find the inverse of a function, you need to swap the x and y values and solve for y.
Q: What is the inverse of a function?
A: The inverse of a function is a function that undoes the original function. It is a function that takes the output value of the original function and returns the input value.
Q: How do I determine if a function is one-to-one?
A: To determine if a function is one-to-one, you need to check if each input corresponds to exactly one output. If each input has a unique output, then the function is one-to-one.
Q: What is the difference between a one-to-one and a many-to-one function?
A: A one-to-one function is a function where each input corresponds to exactly one output. A many-to-one function is a function where each input corresponds to more than one output.
Q: How do I find the domain and range of a function?
A: To find the domain and range of a function, you need to examine the function and determine the set of all possible input and output values.
Q: What is the difference between a function and a relation?
A: A function is a relation where each input corresponds to exactly one output. A relation, on the other hand, is a set of ordered pairs where each input may correspond to more than one output.
Additional Resources
Practice Problems
- Evaluate the function f(x) = 2x + 1 for x = 3.
- Evaluate the function g(x) = x^2 - 4 for x = -2.
- Evaluate the function h(x) = x^3 - 2x^2 + x + 1 for x = 2.
Conclusion
In conclusion, understanding functions and how to evaluate them is crucial for solving problems in various fields. By following the steps outlined in this article, you can select the correct answer when given a table of values. Remember to check the domain and range of the function, use the correct table of values, and look up the output value for the given input.