Given The Function F ( X ) = − X 2 + 15 X F(x) = -x^2 + 15x F ( X ) = − X 2 + 15 X , Evaluate F ( 2 H F(2h F ( 2 H ].

Introduction

In mathematics, functions are a fundamental concept that helps us describe relationships between variables. Evaluating functions is an essential skill that allows us to find the output value of a function for a given input value. In this article, we will focus on evaluating the function $f(x) = -x^2 + 15x$ at the point $2h$. We will break down the process into simple steps and provide a clear explanation of each step.

Understanding the Function

Before we can evaluate the function, we need to understand its structure. The function $f(x) = -x^2 + 15x$ is a quadratic function, which means it has a squared term. The coefficient of the squared term is negative, which means the parabola opens downwards. The function has a single variable, $x$, and the output value depends on the input value of $x$.

Evaluating the Function at $2h$

To evaluate the function at $2h$, we need to substitute $2h$ into the function in place of $x$. This means we will replace every instance of $x$ with $2h$.

$f(2h) = -(2h)^2 + 15(2h)$

Simplifying the Expression

Now that we have substituted $2h$ into the function, we need to simplify the expression. We can start by expanding the squared term.

$f(2h) = -(4h^2) + 30h$

Next, we can combine like terms.

$f(2h) = -4h^2 + 30h$

Final Answer

The final answer is $-4h^2 + 30h$. This is the value of the function $f(x) = -x^2 + 15x$ at the point $2h$.

Conclusion

Evaluating functions is an essential skill in mathematics that allows us to find the output value of a function for a given input value. In this article, we evaluated the function $f(x) = -x^2 + 15x$ at the point $2h$ and simplified the expression to find the final answer. We hope this article has provided a clear explanation of the process and has helped you understand how to evaluate functions.

Step-by-Step Guide

Here is a step-by-step guide to evaluating the function $f(x) = -x^2 + 15x$ at the point $2h$:

1. Substitute $2h$ into the function: Replace every instance of $x$ with $2h$.
2. Simplify the expression: Expand the squared term and combine like terms.
3. Final answer: The final answer is the simplified expression.

Common Mistakes

Here are some common mistakes to avoid when evaluating functions:

• Not substituting the input value: Make sure to substitute the input value into the function.
• Not simplifying the expression: Make sure to simplify the expression after substituting the input value.
• Not combining like terms: Make sure to combine like terms after simplifying the expression.

Real-World Applications

Evaluating functions has many real-world applications, including:

• Physics: Evaluating functions is used to describe the motion of objects and predict their behavior.
• Engineering: Evaluating functions is used to design and optimize systems.
• Economics: Evaluating functions is used to model economic systems and predict economic behavior.

Conclusion

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Introduction

In our previous article, we discussed how to evaluate the function $f(x) = -x^2 + 15x$ at the point $2h$. We provided a step-by-step guide and explained the process in detail. However, we know that sometimes the best way to learn is through questions and answers. In this article, we will provide a Q&A guide to help you understand how to evaluate functions.

Q: What is a function?

A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). It is a way of describing a relationship between variables.

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

A: A function is a relation between a set of inputs and a set of possible outputs, whereas an equation is a statement that two expressions are equal. For example, $f(x) = -x^2 + 15x$ is a function, whereas $x^2 - 15x = 0$ is an equation.

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

A: To evaluate a function at a given point, you need to substitute the input value into the function and simplify the expression. For example, to evaluate the function $f(x) = -x^2 + 15x$ at the point $2h$, you would substitute $2h$ into the function and simplify the expression.

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

A: A function is a relation between a set of inputs and a set of possible outputs, whereas a formula is a mathematical expression that describes a relationship between variables. For example, $f(x) = -x^2 + 15x$ is a function, whereas $y = -x^2 + 15x$ is a formula.

Q: Can I evaluate a function at a point that is not in the domain?

A: No, you cannot evaluate a function at a point that is not in the domain. The domain of a function is the set of all possible input values, and you can only evaluate a function at points that are in the domain.

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

A: To determine if a function is defined at a given point, you need to check if the input value is in the domain of the function. If the input value is in the domain, then the function is defined at that point.

Q: Can I evaluate a function at a point that is in the range?

A: No, you cannot evaluate a function at a point that is in the range. The range of a function is the set of all possible output values, and you can only evaluate a function at points that are in the domain.

Q: How do I know if a function is continuous at a given point?

A: To determine if a function is continuous at a given point, you need to check if the function is defined at that point and if the limit of the function as the input value approaches that point is equal to the output value of the function at that point.

Q: Can I evaluate a function at a point that is not in the range?

A: No, you cannot evaluate a function at a point that is not in the range. The range of a function is the set of all possible output values, and you can only evaluate a function at points that are in the domain.

Conclusion

Evaluating functions is an essential skill in mathematics that allows us to find the output value of a function for a given input value. In this article, we provided a Q&A guide to help you understand how to evaluate functions. We hope this article has provided a clear explanation of the process and has helped you understand how to evaluate functions.

Common Mistakes

Here are some common mistakes to avoid when evaluating functions:

• Not substituting the input value: Make sure to substitute the input value into the function.
• Not simplifying the expression: Make sure to simplify the expression after substituting the input value.
• Not combining like terms: Make sure to combine like terms after simplifying the expression.
• Not checking if the input value is in the domain: Make sure to check if the input value is in the domain of the function.
• Not checking if the function is defined at a given point: Make sure to check if the function is defined at a given point.

Real-World Applications

Evaluating functions has many real-world applications, including:

• Physics: Evaluating functions is used to describe the motion of objects and predict their behavior.
• Engineering: Evaluating functions is used to design and optimize systems.
• Economics: Evaluating functions is used to model economic systems and predict economic behavior.

Conclusion

Evaluating functions is an essential skill in mathematics that allows us to find the output value of a function for a given input value. In this article, we provided a Q&A guide to help you understand how to evaluate functions. We hope this article has provided a clear explanation of the process and has helped you understand how to evaluate functions.