Use The Function Below To Find $f(-2)$.$f(x) = 3^x$A. \$\frac{1}{9}$[/tex\] B. -6 C. -9 D. $\frac{1}{6}$

Introduction

Exponential functions are a fundamental concept in mathematics, and understanding how to evaluate them is crucial for solving various mathematical problems. In this article, we will focus on evaluating the exponential function $f(x) = 3^x$ at a specific value of $x$, namely $x = -2$. We will use the given function to find $f(-2)$ and explore the properties of exponential functions.

What are Exponential Functions?

Exponential functions are a type of mathematical function that describes a relationship between two variables, typically denoted as $x$ and $y$. The general form of an exponential function is $f(x) = a^x$, where $a$ is a positive constant and $x$ is the variable. In our case, the function is $f(x) = 3^x$, where $a = 3$.

Evaluating Exponential Functions

To evaluate an exponential function at a specific value of $x$, we simply substitute the value of $x$ into the function and perform the necessary calculations. In this case, we need to find $f(-2)$, which means we need to substitute $x = -2$ into the function $f(x) = 3^x$.

Step-by-Step Solution

To find $f(-2)$, we follow these steps:

1. Substitute $x = -2$ into the function: We replace $x$ with $-2$ in the function $f(x) = 3^x$.
2. Simplify the expression: We simplify the resulting expression to obtain the final value of $f(-2)$.

Step 1: Substitute $x = -2$ into the function

$f(-2) = 3^{-2}$

Step 2: Simplify the expression

To simplify the expression, we can use the property of exponents that states $a^{-n} = \frac{1}{a^n}$. Applying this property to our expression, we get:

$f(-2) = \frac{1}{3^2}$

Simplifying Further

We can simplify the expression further by evaluating the exponent:

$f(-2) = \frac{1}{9}$

Conclusion

In this article, we used the function $f(x) = 3^x$ to find $f(-2)$. We followed a step-by-step approach to substitute $x = -2$ into the function and simplify the resulting expression. The final value of $f(-2)$ is $\frac{1}{9}$.

Answer

The correct answer is:

A. $\frac{1}{9}$

Discussion

Exponential functions are a fundamental concept in mathematics, and understanding how to evaluate them is crucial for solving various mathematical problems. In this article, we used the function $f(x) = 3^x$ to find $f(-2)$ and explored the properties of exponential functions. We hope this article has provided a clear and concise explanation of how to evaluate exponential functions.

Related Topics

• Exponential functions
• Evaluating exponential functions
• Properties of exponential functions
• Mathematical functions

References

• [1] "Exponential Functions" by Math Open Reference
• [2] "Evaluating Exponential Functions" by Khan Academy
• [3] "Properties of Exponential Functions" by Wolfram MathWorld
  Evaluating Exponential Functions: A Q&A Guide =====================================================

Introduction

In our previous article, we explored the concept of exponential functions and how to evaluate them. We used the function $f(x) = 3^x$ to find $f(-2)$ and simplified the expression to obtain the final value. In this article, we will continue to explore exponential functions and answer some frequently asked questions.

Q&A

Q: What is an exponential function?

A: An exponential function is a type of mathematical function that describes a relationship between two variables, typically denoted as $x$ and $y$. The general form of an exponential function is $f(x) = a^x$, where $a$ is a positive constant and $x$ is the variable.

Q: How do I evaluate an exponential function?

A: To evaluate an exponential function, you simply substitute the value of $x$ into the function and perform the necessary calculations. For example, to find $f(-2)$, you would substitute $x = -2$ into the function $f(x) = 3^x$.

Q: What is the property of exponents that states $a^{-n} = \frac{1}{a^n}$?

A: This property is known as the negative exponent property. It states that for any positive constant $a$ and any integer $n$, $a^{-n} = \frac{1}{a^n}$.

Q: How do I simplify an expression with a negative exponent?

A: To simplify an expression with a negative exponent, you can use the negative exponent property. For example, to simplify the expression $f(-2) = \frac{1}{3^2}$, you would use the negative exponent property to rewrite it as $f(-2) = 3^{-2}$.

Q: What is the final value of $f(-2)$?

A: The final value of $f(-2)$ is $\frac{1}{9}$.

Q: Can I use the function $f(x) = 3^x$ to find $f(2)$?

A: Yes, you can use the function $f(x) = 3^x$ to find $f(2)$. To do this, you would substitute $x = 2$ into the function and perform the necessary calculations.

Q: How do I evaluate $f(2)$?

A: To evaluate $f(2)$, you would substitute $x = 2$ into the function $f(x) = 3^x$. This would give you $f(2) = 3^2$, which simplifies to $f(2) = 9$.

Q: What is the relationship between $f(-2)$ and $f(2)$?

A: The relationship between $f(-2)$ and $f(2)$ is that they are reciprocals of each other. This means that $f(-2) = \frac{1}{f(2)}$.

Q: Can I use the function $f(x) = 3^x$ to find $f(-x)$?

A: Yes, you can use the function $f(x) = 3^x$ to find $f(-x)$. To do this, you would substitute $x = -x$ into the function and perform the necessary calculations.

Q: How do I evaluate $f(-x)$?

A: To evaluate $f(-x)$, you would substitute $x = -x$ into the function $f(x) = 3^x$. This would give you $f(-x) = 3^{-x}$.

Q: What is the relationship between $f(x)$ and $f(-x)$?

A: The relationship between $f(x)$ and $f(-x)$ is that they are reciprocals of each other. This means that $f(-x) = \frac{1}{f(x)}$.

Conclusion

In this article, we answered some frequently asked questions about exponential functions and how to evaluate them. We hope this article has provided a clear and concise explanation of the concepts and has helped to clarify any confusion.

Related Topics

• Exponential functions
• Evaluating exponential functions
• Properties of exponential functions
• Mathematical functions

References

• [1] "Exponential Functions" by Math Open Reference
• [2] "Evaluating Exponential Functions" by Khan Academy
• [3] "Properties of Exponential Functions" by Wolfram MathWorld