Exploring the Function Fx x^2 - x - 6 / (x - 3) at x 5: A Step-by-Step Guide

Introduction

When working with functions in algebra, we frequently need to evaluate expressions for specific values of the variable. This process is called function evaluation. In this guide, we will explore the evaluation of the function F(x) x^2 - x - 6 / (x - 3) at specific values of x, focusing on x 5. We will walk through the steps in detail and use an online graphing tool called Desmos for visualization.

Evaluation of Fx at x 5

Finding F(5)

To evaluate the function F(x) x^2 - x - 6 / (x - 3) at x 5, we need to substitute the value 5 for x in the function and simplify the expression step by step.

Step-by-Step Process

Substitute x 5 into the function: F(5) 5^2 - 5 - 6 / (5 - 3). Calculate the square of 5: F(5) 25 - 5 - 6 / 2. Simplify: F(5) 25 - 5 - 3. Perform the subtraction: F(5) 20 - 3 17.

Verification with Desmos

To verify our calculations, we can use Desmos, an excellent online graphing calculator. The following is the algebraic form of the function and the substitution:

F(x) x^2 - x - 6 / (x - 3)

F(5) 5^2 - 5 - 6 / (5 - 3)

When you input this into Desmos, it will evaluate the function at x 5, and you will see that the result is indeed 17.

Graphical Representation

The function F(x) x^2 - x - 6 / (x - 3) can be graphed to visualize its behavior over a range of x-values. Let's explore the graph and the value at x 5.

Desmos Graph

The Desmos graph of the function F(x) x^2 - x - 6 / (x - 3) is as follows:

Desmos Graph:

From the graph, we can observe the value of the function at various points, including x 5. When x 5, the function value is 17, as calculated earlier.

Conclusion

By evaluating the function F(x) x^2 - x - 6 / (x - 3) at x 5, we have shown that F(5) 17. This was calculated through algebraic simplification and verified using Desmos. Understanding how to evaluate functions and using graphing tools such as Desmos can greatly enhance your algebraic skills and provide deeper insight into the behavior of mathematical functions.

Further Resources

For more practice and resources in algebra, you may want to explore additional topics:

Function evaluation Algebraic simplification Using Desmos for graphing and exploration Step-by-step guides for algebraic expressions

Remember, practice is key to mastering algebraic concepts and techniques.

Keywords

function evaluation, algebraic simplification, Desmos graph