Which Statements Accurately Describe The Function $f(x) = 3(\sqrt{18})^x$? Select Three Options.A. The Domain Is All Real Numbers.B. The Range Is $y \ \textgreater \ 3$.C. The Initial Value Is 3.D. The Initial Value Is 9.E. The

Introduction

When dealing with functions, it's essential to understand their properties, such as domain, range, and initial values. In this article, we will analyze the function $f(x) = 3(\sqrt{18})^x$ and determine which statements accurately describe its function.

Analyzing the Function

The given function is $f(x) = 3(\sqrt{18})^x$. To understand its properties, let's break it down:

• The function is a power function with base $\sqrt{18}$ and exponent $x$.
• The coefficient of the function is 3.

Domain of the Function

The domain of a function is the set of all possible input values for which the function is defined. In the case of the function $f(x) = 3(\sqrt{18})^x$, the base $\sqrt{18}$ is always positive, and the exponent $x$ can be any real number. Therefore, the domain of the function is all real numbers.

Range of the Function

The range of a function is the set of all possible output values for which the function is defined. Since the base $\sqrt{18}$ is always positive, the function $f(x) = 3(\sqrt{18})^x$ will always produce positive values. However, the range is not limited to a specific value, as the function can produce any positive value. Therefore, the range of the function is $y \ \textgreater \ 0$.

Initial Value of the Function

The initial value of a function is the value of the function when the input is 0. To find the initial value of the function $f(x) = 3(\sqrt{18})^x$, we substitute $x = 0$ into the function:

$f(0) = 3(\sqrt{18})^0$

Since any non-zero number raised to the power of 0 is 1, we have:

$f(0) = 3(1) = 3$

Therefore, the initial value of the function is 3.

Conclusion

In conclusion, the statements that accurately describe the function $f(x) = 3(\sqrt{18})^x$ are:

• The domain is all real numbers.
• The initial value is 3.

The other statements are not accurate descriptions of the function. The range of the function is not limited to a specific value, and the initial value is not 9.

Final Answer

The final answer is:

A. The domain is all real numbers. C. The initial value is 3.

Introduction

In our previous article, we analyzed the function $f(x) = 3(\sqrt{18})^x$ and determined its properties, such as domain, range, and initial value. In this article, we will answer some frequently asked questions about the function.

Q: What is the domain of the function $f(x) = 3(\sqrt{18})^x$?

A: The domain of the function $f(x) = 3(\sqrt{18})^x$ is all real numbers. This is because the base $\sqrt{18}$ is always positive, and the exponent $x$ can be any real number.

Q: What is the range of the function $f(x) = 3(\sqrt{18})^x$?

A: The range of the function $f(x) = 3(\sqrt{18})^x$ is $y \ \textgreater \ 0$. This is because the base $\sqrt{18}$ is always positive, and the function will always produce positive values.

Q: What is the initial value of the function $f(x) = 3(\sqrt{18})^x$?

A: The initial value of the function $f(x) = 3(\sqrt{18})^x$ is 3. This is because when we substitute $x = 0$ into the function, we get $f(0) = 3(\sqrt{18})^0 = 3(1) = 3$.

Q: Can the function $f(x) = 3(\sqrt{18})^x$ produce negative values?

A: No, the function $f(x) = 3(\sqrt{18})^x$ cannot produce negative values. This is because the base $\sqrt{18}$ is always positive, and the function will always produce positive values.

Q: Is the function $f(x) = 3(\sqrt{18})^x$ an exponential function?

A: Yes, the function $f(x) = 3(\sqrt{18})^x$ is an exponential function. This is because it has the form $f(x) = ab^x$, where $a$ is the initial value and $b$ is the base.

Q: Can the function $f(x) = 3(\sqrt{18})^x$ be used to model real-world phenomena?

A: Yes, the function $f(x) = 3(\sqrt{18})^x$ can be used to model real-world phenomena. For example, it can be used to model population growth, chemical reactions, or other processes that involve exponential growth or decay.

Conclusion

In conclusion, the function $f(x) = 3(\sqrt{18})^x$ is a powerful tool that can be used to model real-world phenomena. Its properties, such as domain, range, and initial value, make it a useful function to study and apply in various fields.

Final Answer

The final answer is:

• The domain of the function $f(x) = 3(\sqrt{18})^x$ is all real numbers.
• The range of the function $f(x) = 3(\sqrt{18})^x$ is $y \ \textgreater \ 0$.
• The initial value of the function $f(x) = 3(\sqrt{18})^x$ is 3.
• The function $f(x) = 3(\sqrt{18})^x$ is an exponential function.
• The function $f(x) = 3(\sqrt{18})^x$ can be used to model real-world phenomena.