Given The Function $f(x) = -2(7)^x$, Evaluate The Function For Specific Values Of $x$ Or Analyze Its Properties.

$$

Introduction

In mathematics, functions are used to describe the relationship between variables. They can be used to model real-world situations, make predictions, and solve problems. In this article, we will evaluate and analyze the function $f(x) = -2(7)^x$. We will explore its properties, evaluate it for specific values of $x$, and discuss its behavior.

Evaluating the Function for Specific Values of $x$

To evaluate the function $f(x) = -2(7)^x$ for specific values of $x$, we can simply substitute the value of $x$ into the function. Let's evaluate the function for $x = 0$, $x = 1$, and $x = 2$.

Evaluating the Function for $x = 0$

When $x = 0$, the function becomes:

$f(0) = -2(7)^0$

Since any number raised to the power of 0 is equal to 1, we have:

$f(0) = -2(1)$

$f(0) = -2$

So, the value of the function at $x = 0$ is $-2$.

Evaluating the Function for $x = 1$

When $x = 1$, the function becomes:

$f(1) = -2(7)^1$

Since any number raised to the power of 1 is equal to itself, we have:

$f(1) = -2(7)$

$f(1) = -14$

So, the value of the function at $x = 1$ is $-14$.

Evaluating the Function for $x = 2$

When $x = 2$, the function becomes:

$f(2) = -2(7)^2$

Since any number raised to the power of 2 is equal to the square of the number, we have:

$f(2) = -2(49)$

$f(2) = -98$

So, the value of the function at $x = 2$ is $-98$.

Analyzing the Properties of the Function

Now that we have evaluated the function for specific values of $x$, let's analyze its properties.

Domain and Range

The domain of a function is the set of all possible input values, while the range is the set of all possible output values. In this case, the domain of the function $f(x) = -2(7)^x$ is all real numbers, since $x$ can take on any value. The range of the function is also all real numbers, since the output of the function can be any real number.

Exponential Growth

The function $f(x) = -2(7)^x$ is an exponential function, which means that it grows rapidly as $x$ increases. In fact, the function grows exponentially, meaning that the output of the function increases by a factor of 7 for each increase in $x$ by 1.

Asymptotes

An asymptote is a line that the graph of a function approaches as $x$ approaches a certain value. In this case, the function $f(x) = -2(7)^x$ has a horizontal asymptote at $y = 0$, since the function approaches 0 as $x$ approaches negative infinity.

Graphing the Function

To graph the function $f(x) = -2(7)^x$, we can use a graphing calculator or software. The graph of the function is a curve that approaches the horizontal asymptote at $y = 0$ as $x$ approaches negative infinity.

Conclusion

In this article, we evaluated and analyzed the function $f(x) = -2(7)^x$. We explored its properties, evaluated it for specific values of $x$, and discussed its behavior. We found that the function is an exponential function that grows rapidly as $x$ increases, and that it has a horizontal asymptote at $y = 0$. We also graphed the function using a graphing calculator or software.

$$

Introduction

In our previous article, we evaluated and analyzed the function $f(x) = -2(7)^x$. We explored its properties, evaluated it for specific values of $x$, and discussed its behavior. In this article, we will answer some frequently asked questions about the function.

Q: What is the domain of the function $f(x) = -2(7)^x$?

A: The domain of the function $f(x) = -2(7)^x$ is all real numbers, since $x$ can take on any value.

Q: What is the range of the function $f(x) = -2(7)^x$?

A: The range of the function $f(x) = -2(7)^x$ is also all real numbers, since the output of the function can be any real number.

Q: Is the function $f(x) = -2(7)^x$ an exponential function?

A: Yes, the function $f(x) = -2(7)^x$ is an exponential function, which means that it grows rapidly as $x$ increases.

Q: What is the horizontal asymptote of the function $f(x) = -2(7)^x$?

A: The horizontal asymptote of the function $f(x) = -2(7)^x$ is $y = 0$, since the function approaches 0 as $x$ approaches negative infinity.

Q: How do I graph the function $f(x) = -2(7)^x$?

A: You can graph the function $f(x) = -2(7)^x$ using a graphing calculator or software. The graph of the function is a curve that approaches the horizontal asymptote at $y = 0$ as $x$ approaches negative infinity.

Q: Can I use the function $f(x) = -2(7)^x$ to model real-world situations?

A: Yes, the function $f(x) = -2(7)^x$ can be used to model real-world situations where exponential growth is involved. For example, you can use this function to model the growth of a population, the spread of a disease, or the growth of a company.

Q: How do I evaluate the function $f(x) = -2(7)^x$ for specific values of $x$?

A: To evaluate the function $f(x) = -2(7)^x$ for specific values of $x$, you can simply substitute the value of $x$ into the function. For example, to evaluate the function at $x = 0$, you would substitute $x = 0$ into the function and simplify.

Q: What are some common mistakes to avoid when working with the function $f(x) = -2(7)^x$?

A: Some common mistakes to avoid when working with the function $f(x) = -2(7)^x$ include:

• Not using the correct order of operations when evaluating the function
• Not simplifying the function correctly
• Not using the correct domain and range of the function
• Not graphing the function correctly

Conclusion

In this article, we answered some frequently asked questions about the function $f(x) = -2(7)^x$. We covered topics such as the domain and range of the function, its exponential growth, and how to graph the function. We also provided some tips and common mistakes to avoid when working with the function.