Add the constant and the simplified fraction

Oct 13, 2025 by pynkocean.com 0 views

$Add the constant and the simplified fraction$

Understanding the Function Rule

The function rule provided is $f(x) = 8 + \frac{x}{15}$ , where $x$ is the input value and $f(x)$ is the output value. This function rule represents a linear equation, where the output value is a constant (8) plus a fraction of the input value ( $\frac{x}{15}$ ).

Applying the Function Rule to Find f(45)

To find the value of $f(45)$ , we need to substitute $x = 45$ into the function rule. This means we will replace every instance of $x$ with 45 and then simplify the expression.

Step-by-Step Calculation

Substitute x = 45 into the function rule: $f(45) = 8 + \frac{45}{15}$
Simplify the fraction: $\frac{45}{15} = 3$
Add the constant and the simplified fraction: $f(45) = 8 + 3$
Calculate the final value: $f(45) = 11$

Conclusion

Using the function rule $f(x) = 8 + \frac{x}{15}$ , we have found that $f(45) = 11$ . This means that when the input value is 45, the output value of the function is 11.

Interpreting the Result

The result $f(45) = 11$ can be interpreted in various ways, depending on the context in which the function is being used. For example, if the function represents a linear model of a physical system, the output value of 11 might represent a specific measurement or quantity.

Real-World Applications

The function rule $f(x) = 8 + \frac{x}{15}$ has various real-world applications, such as modeling population growth, predicting stock prices, or optimizing resource allocation. By understanding how to apply the function rule to find specific values, we can gain insights into the behavior of complex systems and make informed decisions.

Common Mistakes to Avoid

When working with function rules, it's essential to avoid common mistakes such as:

Incorrect substitution: Failing to substitute the correct value of $x$ into the function rule.
Insufficient simplification: Failing to simplify the expression after substitution.
Incorrect calculation: Failing to perform the correct arithmetic operations.

Best Practices

To ensure accurate results when working with function rules, follow these best practices:

Read the function rule carefully: Understand the structure and syntax of the function rule.
Substitute values correctly: Replace every instance of $x$ with the correct value.
Simplify expressions thoroughly: Ensure that all fractions and expressions are simplified correctly.
Perform arithmetic operations accurately: Double-check your calculations to avoid errors.

Conclusion

In conclusion, finding the value of $f(45)$ using the function rule $f(x) = 8 + \frac{x}{15}$ requires careful substitution, simplification, and calculation. By following best practices and avoiding common mistakes, we can ensure accurate results and gain insights into the behavior of complex systems.

Q: What is the function rule used to find f(45)?

A: The function rule used to find f(45) is $f(x) = 8 + \frac{x}{15}$ .

Q: How do I substitute x = 45 into the function rule?

A: To substitute x = 45 into the function rule, replace every instance of x with 45. This means that the function rule becomes $f(45) = 8 + \frac{45}{15}$ .

Q: What is the simplified fraction of $\frac{45}{15}$ ?

A: The simplified fraction of $\frac{45}{15}$ is 3.

Q: How do I add the constant and the simplified fraction to find f(45)?

A: To add the constant and the simplified fraction, combine the two values: $f(45) = 8 + 3$ .

Q: What is the final value of f(45)?

A: The final value of f(45) is 11.

Q: Can I use the function rule to find the value of f(x) for any value of x?

A: Yes, you can use the function rule to find the value of f(x) for any value of x. Simply substitute the value of x into the function rule and follow the same steps as before.

Q: What are some real-world applications of the function rule f(x) = 8 + $\frac{x}{15}$ ?

A: Some real-world applications of the function rule f(x) = 8 + $\frac{x}{15}$ include modeling population growth, predicting stock prices, and optimizing resource allocation.

Q: What are some common mistakes to avoid when working with function rules?

A: Some common mistakes to avoid when working with function rules include:

Incorrect substitution
Insufficient simplification
Incorrect calculation

Q: How can I ensure accurate results when working with function rules?

A: To ensure accurate results when working with function rules, follow these best practices:

Read the function rule carefully
Substitute values correctly
Simplify expressions thoroughly
Perform arithmetic operations accurately

Q: Can I use the function rule to find the value of f(x) for negative values of x?

A: Yes, you can use the function rule to find the value of f(x) for negative values of x. However, keep in mind that the function rule is a linear equation, and the output value will be a constant plus a fraction of the input value.

Q: How can I graph the function rule f(x) = 8 + $\frac{x}{15}$ ?

A: To graph the function rule f(x) = 8 + $\frac{x}{15}$ , plot the points (x, f(x)) for various values of x and connect the points with a straight line.

Q: Can I use the function rule to find the value of f(x) for non-integer values of x?

A: Yes, you can use the function rule to find the value of f(x) for non-integer values of x. Simply substitute the non-integer value of x into the function rule and follow the same steps as before.

Q: How can I use the function rule to model real-world phenomena?

A: To use the function rule to model real-world phenomena, identify the input and output values of the function and substitute them into the function rule. Then, use the resulting equation to make predictions or analyze the behavior of the system.