Given The Function F ( X ) = 15 X 4 − 5 X 2 + 9 X − 1 F(x) = 15x^4 - 5x^2 + 9x - 1 F ( X ) = 15 X 4 − 5 X 2 + 9 X − 1 Over The Interval − 3 , 0 {-3,0} − 3 , 0 ,Enter The Value Of F ( − 3 F(-3 F ( − 3 ].$f(-3) = $\square$ (Simplify.)

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Evaluating the Function f(x) = 15x^4 - 5x^2 + 9x - 1 at x = -3

In this article, we will evaluate the function f(x) = 15x^4 - 5x^2 + 9x - 1 at x = -3. This involves substituting the value of x into the function and simplifying the resulting expression. We will also discuss the importance of evaluating functions at specific points and how it is used in various mathematical applications.

Understanding the Function

The given function is a polynomial of degree 4, which means it has a term with x raised to the power of 4. The function is defined as f(x) = 15x^4 - 5x^2 + 9x - 1. To evaluate this function at x = -3, we need to substitute x = -3 into the function and simplify the resulting expression.

Substituting x = -3 into the Function

To evaluate the function at x = -3, we substitute x = -3 into the function f(x) = 15x^4 - 5x^2 + 9x - 1. This gives us:

f(-3) = 15(-3)^4 - 5(-3)^2 + 9(-3) - 1

Simplifying the Expression

To simplify the expression, we need to evaluate the powers of -3. We have:

(-3)^4 = 81 (-3)^2 = 9

Substituting these values into the expression, we get:

f(-3) = 15(81) - 5(9) + 9(-3) - 1 f(-3) = 1215 - 45 - 27 - 1 f(-3) = 1142

Conclusion

In this article, we evaluated the function f(x) = 15x^4 - 5x^2 + 9x - 1 at x = -3. We substituted x = -3 into the function and simplified the resulting expression to get f(-3) = 1142. This demonstrates the importance of evaluating functions at specific points and how it is used in various mathematical applications.

Importance of Evaluating Functions

Evaluating functions at specific points is an essential concept in mathematics. It is used in various mathematical applications, such as:

  • Graphing functions: Evaluating functions at specific points helps us understand the behavior of the function and create accurate graphs.
  • Optimization problems: Evaluating functions at specific points is used to find the maximum or minimum value of a function.
  • Physics and engineering: Evaluating functions at specific points is used to model real-world phenomena and make predictions.

Real-World Applications

Evaluating functions at specific points has numerous real-world applications. Some examples include:

  • Designing buildings: Architects use mathematical models to design buildings. Evaluating functions at specific points helps them create accurate models and make predictions about the behavior of the building.
  • Predicting stock prices: Financial analysts use mathematical models to predict stock prices. Evaluating functions at specific points helps them make accurate predictions and make informed investment decisions.
  • Modeling population growth: Biologists use mathematical models to study population growth. Evaluating functions at specific points helps them understand the behavior of the population and make predictions about future growth.

Conclusion

In conclusion, evaluating the function f(x) = 15x^4 - 5x^2 + 9x - 1 at x = -3 involves substituting x = -3 into the function and simplifying the resulting expression. This demonstrates the importance of evaluating functions at specific points and how it is used in various mathematical applications.
Evaluating the Function f(x) = 15x^4 - 5x^2 + 9x - 1 at x = -3: Q&A

In our previous article, we evaluated the function f(x) = 15x^4 - 5x^2 + 9x - 1 at x = -3. We substituted x = -3 into the function and simplified the resulting expression to get f(-3) = 1142. In this article, we will answer some frequently asked questions about evaluating functions at specific points.

Q: What is the importance of evaluating functions at specific points?

A: Evaluating functions at specific points is an essential concept in mathematics. It is used in various mathematical applications, such as graphing functions, optimization problems, and physics and engineering.

Q: How do I evaluate a function at a specific point?

A: To evaluate a function at a specific point, you need to substitute the value of x into the function and simplify the resulting expression.

Q: What is the difference between evaluating a function at a specific point and finding the derivative of a function?

A: Evaluating a function at a specific point involves substituting the value of x into the function and simplifying the resulting expression. Finding the derivative of a function involves finding the rate of change of the function with respect to x.

Q: Can I use a calculator to evaluate a function at a specific point?

A: Yes, you can use a calculator to evaluate a function at a specific point. However, it is also important to understand the underlying mathematics and be able to evaluate the function by hand.

Q: How do I know if I have evaluated a function correctly at a specific point?

A: To ensure that you have evaluated a function correctly at a specific point, you need to check your work and make sure that you have followed the correct steps.

Q: What are some common mistakes to avoid when evaluating functions at specific points?

A: Some common mistakes to avoid when evaluating functions at specific points include:

  • Not following the order of operations: Make sure to follow the order of operations (PEMDAS) when evaluating a function.
  • Not simplifying the expression: Make sure to simplify the expression after substituting the value of x into the function.
  • Not checking your work: Make sure to check your work and make sure that you have followed the correct steps.

Q: Can I use technology to help me evaluate functions at specific points?

A: Yes, you can use technology to help you evaluate functions at specific points. Some examples include:

  • Graphing calculators: Graphing calculators can help you visualize the function and evaluate it at specific points.
  • Computer algebra systems: Computer algebra systems can help you evaluate functions at specific points and simplify the resulting expression.
  • Online calculators: Online calculators can help you evaluate functions at specific points and provide step-by-step solutions.

Conclusion

In conclusion, evaluating the function f(x) = 15x^4 - 5x^2 + 9x - 1 at x = -3 involves substituting x = -3 into the function and simplifying the resulting expression. We have also answered some frequently asked questions about evaluating functions at specific points. By following the correct steps and avoiding common mistakes, you can evaluate functions at specific points with confidence.