F(x=)5x + 4 , Find F(3) + F(- 3) )

Mar 9, 2025 by ADMIN 35 views

Evaluating the Function f(x) = 5x + 4 and Finding f(3) + f(-3)

In mathematics, functions are used to describe the relationship between variables. A function is a rule that assigns to each input value, or independent variable, a unique output value, or dependent variable. In this article, we will explore the function f(x) = 5x + 4 and evaluate its values at x = 3 and x = -3.

Understanding the Function f(x) = 5x + 4

The given function is f(x) = 5x + 4. This function takes an input value x and returns an output value that is 5 times x plus 4. To evaluate the function at a specific value of x, we simply substitute the value of x into the function and perform the necessary calculations.

Evaluating f(3)

To evaluate f(3), we substitute x = 3 into the function f(x) = 5x + 4.

f(3) = 5(3) + 4 f(3) = 15 + 4 f(3) = 19

Therefore, the value of f(3) is 19.

Evaluating f(-3)

To evaluate f(-3), we substitute x = -3 into the function f(x) = 5x + 4.

f(-3) = 5(-3) + 4 f(-3) = -15 + 4 f(-3) = -11

Therefore, the value of f(-3) is -11.

Finding f(3) + f(-3)

Now that we have evaluated f(3) and f(-3), we can find their sum.

f(3) + f(-3) = 19 + (-11) f(3) + f(-3) = 8

Therefore, the value of f(3) + f(-3) is 8.

In this article, we evaluated the function f(x) = 5x + 4 at x = 3 and x = -3, and found their sum. We used the function definition to substitute the values of x into the function and perform the necessary calculations. The value of f(3) was found to be 19, and the value of f(-3) was found to be -11. The sum of f(3) and f(-3) was found to be 8.

Key Takeaways

The function f(x) = 5x + 4 takes an input value x and returns an output value that is 5 times x plus 4.
To evaluate the function at a specific value of x, we substitute the value of x into the function and perform the necessary calculations.
The value of f(3) is 19.
The value of f(-3) is -11.
The sum of f(3) and f(-3) is 8.

Real-World Applications

Functions like f(x) = 5x + 4 have many real-world applications in fields such as physics, engineering, and economics. For example, in physics, the function might represent the relationship between the distance traveled by an object and the time it takes to travel that distance. In engineering, the function might represent the relationship between the voltage applied to a circuit and the current flowing through it. In economics, the function might represent the relationship between the price of a good and the quantity demanded.

Future Directions

In the future, we can explore more complex functions and their applications in various fields. We can also investigate the properties of functions, such as their domain and range, and how they can be used to model real-world phenomena.

References

[1] "Functions" by Khan Academy
[2] "Algebra" by MIT OpenCourseWare
[3] "Calculus" by Stanford University

In our previous article, we explored the function f(x) = 5x + 4 and evaluated its values at x = 3 and x = -3. We found that f(3) = 19 and f(-3) = -11, and the sum of f(3) and f(-3) was 8. In this article, we will answer some frequently asked questions about the function f(x) = 5x + 4 and its evaluation.

Q: What is the function f(x) = 5x + 4?

A: The function f(x) = 5x + 4 is a linear function that takes an input value x and returns an output value that is 5 times x plus 4.

Q: How do I evaluate the function f(x) = 5x + 4 at a specific value of x?

A: To evaluate the function f(x) = 5x + 4 at a specific value of x, you simply substitute the value of x into the function and perform the necessary calculations.

Q: What is the value of f(3)?

A: The value of f(3) is 19.

Q: What is the value of f(-3)?

A: The value of f(-3) is -11.

Q: What is the sum of f(3) and f(-3)?

A: The sum of f(3) and f(-3) is 8.

Q: Can I use the function f(x) = 5x + 4 to model real-world phenomena?

A: Yes, the function f(x) = 5x + 4 can be used to model real-world phenomena such as the relationship between the distance traveled by an object and the time it takes to travel that distance, or the relationship between the voltage applied to a circuit and the current flowing through it.

Q: What are some common applications of the function f(x) = 5x + 4?

A: Some common applications of the function f(x) = 5x + 4 include:

Modeling the relationship between the distance traveled by an object and the time it takes to travel that distance.
Modeling the relationship between the voltage applied to a circuit and the current flowing through it.
Modeling the relationship between the price of a good and the quantity demanded.

Q: Can I use the function f(x) = 5x + 4 to solve problems in physics, engineering, and economics?

A: Yes, the function f(x) = 5x + 4 can be used to solve problems in physics, engineering, and economics.

Q: What are some common mistakes to avoid when evaluating the function f(x) = 5x + 4?

A: Some common mistakes to avoid when evaluating the function f(x) = 5x + 4 include:

Not substituting the value of x into the function.
Not performing the necessary calculations.
Not checking the units of the input and output values.

In this article, we answered some frequently asked questions about the function f(x) = 5x + 4 and its evaluation. We hope that this article has been helpful in clarifying any confusion about the function and its applications.

Key Takeaways

The function f(x) = 5x + 4 is a linear function that takes an input value x and returns an output value that is 5 times x plus 4.
To evaluate the function f(x) = 5x + 4 at a specific value of x, you simply substitute the value of x into the function and perform the necessary calculations.
The value of f(3) is 19.
The value of f(-3) is -11.
The sum of f(3) and f(-3) is 8.

Real-World Applications

Future Directions

References

[1] "Functions" by Khan Academy
[2] "Algebra" by MIT OpenCourseWare
[3] "Calculus" by Stanford University

Note: The references provided are for educational purposes only and are not intended to be a comprehensive list of resources.