Given \[$ G(x) \$\], Evaluate \[$ G(-2) \$\].$\[ \begin{array}{l} g(x) = \frac{3x^2 - 2x}{2x} \\ g(-2) = [?] \end{array} \\]

Feb 27, 2025 by ADMIN 125 views

**Evaluating a Function: A Step-by-Step Guide**

Introduction

In mathematics, functions are used to describe the relationship between variables. Evaluating a function at a specific value of the variable is a crucial concept in mathematics. In this article, we will learn how to evaluate a function at a specific value using the given function g(x) = (3x^2 - 2x) / (2x).

Understanding the Function

Before we can evaluate the function at a specific value, we need to understand the function itself. The function g(x) is defined as g(x) = (3x^2 - 2x) / (2x). This function takes a value of x as input and returns a value as output.

Evaluating the Function at x = -2

Now that we have understood the function, let's evaluate it at x = -2. To do this, we need to substitute x = -2 into the function g(x) = (3x^2 - 2x) / (2x).

Step 1: Substitute x = -2 into the function

g(-2) = (3(-2)^2 - 2(-2)) / (2(-2))

Step 2: Simplify the expression

g(-2) = (3(4) + 4) / (-4)

Step 3: Evaluate the expression

g(-2) = (12 + 4) / (-4)

g(-2) = 16 / (-4)

g(-2) = -4

Conclusion

In this article, we learned how to evaluate a function at a specific value using the given function g(x) = (3x^2 - 2x) / (2x). We substituted x = -2 into the function and simplified the expression to get the final value of g(-2) = -4.

Key Takeaways

Evaluating a function at a specific value is a crucial concept in mathematics.
To evaluate a function, we need to substitute the value into the function and simplify the expression.
The function g(x) = (3x^2 - 2x) / (2x) can be evaluated at x = -2 to get the final value of g(-2) = -4.

Real-World Applications

Evaluating functions is a fundamental concept in mathematics that has numerous real-world applications. Some of the real-world applications of evaluating functions include:

Physics: Evaluating functions is used to describe the motion of objects in physics. For example, the position of an object at a specific time can be described using a function.
Engineering: Evaluating functions is used to design and optimize systems in engineering. For example, the stress on a beam can be described using a function.
Economics: Evaluating functions is used to model economic systems in economics. For example, the demand for a product can be described using a function.

Common Mistakes to Avoid

When evaluating functions, there are several common mistakes to avoid. Some of these mistakes include:

Not simplifying the expression: Failing to simplify the expression can lead to incorrect results.
Not substituting the value correctly: Failing to substitute the value correctly can lead to incorrect results.
Not checking the domain: Failing to check the domain of the function can lead to incorrect results.

Conclusion

Introduction

In our previous article, we learned how to evaluate a function at a specific value using the given function g(x) = (3x^2 - 2x) / (2x). In this article, we will answer some frequently asked questions about evaluating functions.

Q&A

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

A: Evaluating a function involves finding the value of the function at a specific point, whereas finding the derivative of a function involves finding the rate of change of the function at a specific point.

Q: How do I know if a function is defined at a specific point?

A: A function is defined at a specific point if the denominator of the function is not equal to zero at that point. In other words, if the function is a rational function, it is defined at a point if the denominator is not equal to zero at that point.

Q: What is the difference between a function and a relation?

A: A function is a relation between a set of inputs (called the domain) and a set of outputs (called the range) where each input corresponds to exactly one output. A relation, on the other hand, is a set of ordered pairs where each input may correspond to more than one output.

Q: How do I evaluate a function with a square root in the denominator?

A: To evaluate a function with a square root in the denominator, you need to rationalize the denominator by multiplying both the numerator and the denominator by the square root of the denominator.

Q: What is the difference between a function and an equation?

A: A function is an equation that assigns a unique output to each input, whereas an equation is a statement that two expressions are equal.

Q: How do I evaluate a function with a fraction in the numerator?

A: To evaluate a function with a fraction in the numerator, you need to simplify the fraction by dividing the numerator and the denominator by their greatest common divisor.

Q: What is the difference between a function and a formula?

A: A function is a mathematical relationship between a set of inputs and a set of outputs, whereas a formula is a mathematical expression that describes a specific relationship between variables.

Q: How do I evaluate a function with a negative exponent?

A: To evaluate a function with a negative exponent, you need to rewrite the exponent as a positive exponent by taking the reciprocal of the base.

Q: What is the difference between a function and a graph?

A: A function is a mathematical relationship between a set of inputs and a set of outputs, whereas a graph is a visual representation of the function.

Q: How do I evaluate a function with a trigonometric function in the denominator?

A: To evaluate a function with a trigonometric function in the denominator, you need to use the trigonometric identity to simplify the expression.

Conclusion

In conclusion, evaluating functions is a crucial concept in mathematics that has numerous real-world applications. By understanding how to evaluate functions, we can describe complex relationships between variables and make informed decisions in various fields. We hope that this Q&A guide has helped to clarify any questions you may have had about evaluating functions.

Common Mistakes to Avoid

When evaluating functions, there are several common mistakes to avoid. Some of these mistakes include:

Not simplifying the expression: Failing to simplify the expression can lead to incorrect results.
Not substituting the value correctly: Failing to substitute the value correctly can lead to incorrect results.
Not checking the domain: Failing to check the domain of the function can lead to incorrect results.

Real-World Applications

Evaluating functions is a fundamental concept in mathematics that has numerous real-world applications. Some of the real-world applications of evaluating functions include:

Physics: Evaluating functions is used to describe the motion of objects in physics. For example, the position of an object at a specific time can be described using a function.
Engineering: Evaluating functions is used to design and optimize systems in engineering. For example, the stress on a beam can be described using a function.
Economics: Evaluating functions is used to model economic systems in economics. For example, the demand for a product can be described using a function.