Evaluating the Expression Inside the Absolute Value Function

Oct 13, 2025 by miodeya.com 21 views

Understanding the Function Rule

In mathematics, a function rule is a mathematical expression that defines a relationship between an input value and an output value. The function rule is often represented as an equation, where the input value is represented by a variable, and the output value is represented by an expression involving the variable. In this article, we will explore the function rule $f(x) = 9|11 - x|$ and evaluate it for a specific input value, $x = 12$ .

The Function Rule: $f(x) = 9|11 - x|$

The function rule $f(x) = 9|11 - x|$ involves the absolute value function, which is denoted by the vertical bars, $| \cdot |$ . The absolute value function returns the distance of a number from zero, without considering its sign. In this case, the absolute value function is used to evaluate the expression $11 - x$ .

Evaluating the Expression Inside the Absolute Value Function

To evaluate the expression inside the absolute value function, we need to substitute the input value, $x = 12$ , into the expression $11 - x$ . This gives us:

11 - 12 = -1

Evaluating the Absolute Value Function

Now that we have evaluated the expression inside the absolute value function, we can evaluate the absolute value function itself. Since the expression $11 - 12 = -1$ is negative, the absolute value function returns the distance of $-1$ from zero, which is $1$ . Therefore, we have:

|11 - 12| = | -1 | = 1

Evaluating the Function Rule

Now that we have evaluated the absolute value function, we can evaluate the function rule $f(x) = 9|11 - x|$ . Substituting the value of the absolute value function, $|11 - 12| = 1$ , into the function rule, we get:

f(12) = 9|11 - 12| = 9(1) = 9

Conclusion

In this article, we evaluated the function rule $f(x) = 9|11 - x|$ for a specific input value, $x = 12$ . We first evaluated the expression inside the absolute value function, then evaluated the absolute value function itself, and finally evaluated the function rule. The result is $f(12) = 9$ .

Key Takeaways

The function rule $f(x) = 9|11 - x|$ involves the absolute value function.
To evaluate the function rule, we need to evaluate the expression inside the absolute value function and then evaluate the absolute value function itself.
The result of evaluating the function rule is $f(12) = 9$ .

Common Mistakes to Avoid

Not evaluating the expression inside the absolute value function before evaluating the absolute value function itself.
Not substituting the input value into the expression inside the absolute value function.
Not evaluating the absolute value function correctly.

Real-World Applications

The function rule $f(x) = 9|11 - x|$ has many real-world applications, including:

Finance: The function rule can be used to calculate the distance between two points in a financial graph.
Science: The function rule can be used to calculate the distance between two points in a scientific graph.
Engineering: The function rule can be used to calculate the distance between two points in an engineering graph.

Conclusion

Q: What is the function rule $f(x) = 9|11 - x|$ ?

A: The function rule $f(x) = 9|11 - x|$ is a mathematical expression that defines a relationship between an input value and an output value. The function rule involves the absolute value function, which is denoted by the vertical bars, $| \cdot |$ .

Q: What is the absolute value function?

A: The absolute value function returns the distance of a number from zero, without considering its sign. In other words, it gives the magnitude of a number.

Q: How do I evaluate the expression inside the absolute value function?

A: To evaluate the expression inside the absolute value function, you need to substitute the input value into the expression. For example, if the input value is $x = 12$ , you would substitute $12$ into the expression $11 - x$ .

Q: How do I evaluate the absolute value function?

A: To evaluate the absolute value function, you need to evaluate the expression inside the absolute value function and then take the absolute value of the result. For example, if the expression inside the absolute value function is $-1$ , the absolute value function would return $| -1 | = 1$ .

Q: What is the result of evaluating the function rule $f(x) = 9|11 - x|$ for $x = 12$ ?

A: The result of evaluating the function rule $f(x) = 9|11 - x|$ for $x = 12$ is $f(12) = 9$ .

Q: What are some common mistakes to avoid when evaluating the function rule?

A: Some common mistakes to avoid when evaluating the function rule include:

Not evaluating the expression inside the absolute value function before evaluating the absolute value function itself.
Not substituting the input value into the expression inside the absolute value function.
Not evaluating the absolute value function correctly.

Q: What are some real-world applications of the function rule $f(x) = 9|11 - x|$ ?

A: Some real-world applications of the function rule $f(x) = 9|11 - x|$ include:

Finance: The function rule can be used to calculate the distance between two points in a financial graph.
Science: The function rule can be used to calculate the distance between two points in a scientific graph.
Engineering: The function rule can be used to calculate the distance between two points in an engineering graph.

Q: How can I use the function rule $f(x) = 9|11 - x|$ in my own work?

A: You can use the function rule $f(x) = 9|11 - x|$ in your own work by substituting different input values into the function rule and evaluating the result. This can be useful in a variety of fields, including finance, science, and engineering.

Q: What are some tips for evaluating the function rule $f(x) = 9|11 - x|$ ?

A: Some tips for evaluating the function rule $f(x) = 9|11 - x|$ include:

Make sure to evaluate the expression inside the absolute value function before evaluating the absolute value function itself.
Make sure to substitute the input value into the expression inside the absolute value function.
Make sure to evaluate the absolute value function correctly.

Conclusion

In conclusion, evaluating the function rule $f(x) = 9|11 - x|$ for a specific input value requires careful evaluation of the expression inside the absolute value function and the absolute value function itself. This article provides a Q&A guide to help you evaluate the function rule and highlights common mistakes to avoid.