Evaluate The Function For Each Input Listed In The Table, And Graph The Resulting Ordered Pairs On The Coordinate Plane.$\[ \begin{tabular}{|c|c|} \hline $x$ & $f(x) = 2^x$ \\ \hline 0 & \\ \hline 1 & \\ \hline 2 & \\ \hline 3 & \\ \hline 4 &

Feb 25, 2025 by ADMIN 243 views

Evaluating the Function $f(x) = 2^x$ for Each Input Listed in the Table and Graphing the Resulting Ordered Pairs on the Coordinate Plane

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Introduction

In this article, we will evaluate the function $f(x) = 2^x$ for each input listed in the table and graph the resulting ordered pairs on the coordinate plane. The function $f(x) = 2^x$ is an exponential function that represents the power of 2 raised to the power of $x$ . This function is commonly used in mathematics and has many real-world applications.

Evaluating the Function for Each Input Listed in the Table

The table lists the input values of $x$ and the corresponding output values of $f(x) = 2^x$ . We will evaluate the function for each input listed in the table.

$x$	$f(x) = 2^x$
0
1
2
3
4

Evaluating $f(0)$

To evaluate $f(0)$ , we substitute $x = 0$ into the function $f(x) = 2^x$ . This gives us:

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

So, the ordered pair $(0, 1)$ is a solution to the equation $f(x) = 2^x$ .

Evaluating $f(1)$

To evaluate $f(1)$ , we substitute $x = 1$ into the function $f(x) = 2^x$ . This gives us:

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

So, the ordered pair $(1, 2)$ is a solution to the equation $f(x) = 2^x$ .

Evaluating $f(2)$

To evaluate $f(2)$ , we substitute $x = 2$ into the function $f(x) = 2^x$ . This gives us:

$f(2) = 2^2 = 4$

So, the ordered pair $(2, 4)$ is a solution to the equation $f(x) = 2^x$ .

Evaluating $f(3)$

To evaluate $f(3)$ , we substitute $x = 3$ into the function $f(x) = 2^x$ . This gives us:

$f(3) = 2^3 = 8$

So, the ordered pair $(3, 8)$ is a solution to the equation $f(x) = 2^x$ .

Evaluating $f(4)$

To evaluate $f(4)$ , we substitute $x = 4$ into the function $f(x) = 2^x$ . This gives us:

$f(4) = 2^4 = 16$

So, the ordered pair $(4, 16)$ is a solution to the equation $f(x) = 2^x$ .

Graphing the Resulting Ordered Pairs on the Coordinate Plane

Now that we have evaluated the function $f(x) = 2^x$ for each input listed in the table, we can graph the resulting ordered pairs on the coordinate plane.

Plotting the Ordered Pairs

To plot the ordered pairs, we will use the following coordinates:

$(0, 1)$
$(1, 2)$
$(2, 4)$
$(3, 8)$
$(4, 16)$

We will plot these points on the coordinate plane and connect them with a smooth curve to form the graph of the function $f(x) = 2^x$ .

Graphing the Function

The graph of the function $f(x) = 2^x$ is an exponential curve that passes through the points $(0, 1)$ , $(1, 2)$ , $(2, 4)$ , $(3, 8)$ , and $(4, 16)$ . The curve is concave upward and has a steep slope as $x$ increases.

Conclusion

In this article, we evaluated the function $f(x) = 2^x$ for each input listed in the table and graphed the resulting ordered pairs on the coordinate plane. We found that the function is an exponential function that represents the power of 2 raised to the power of $x$ . The graph of the function is an exponential curve that passes through the points $(0, 1)$ , $(1, 2)$ , $(2, 4)$ , $(3, 8)$ , and $(4, 16)$ . This function has many real-world applications and is commonly used in mathematics.

Discussion

The function $f(x) = 2^x$ is a simple yet powerful function that has many real-world applications. It is used in mathematics to model exponential growth and decay, and it is also used in science and engineering to model population growth, chemical reactions, and other phenomena.

The function $f(x) = 2^x$ can be used to model many real-world phenomena, including population growth, chemical reactions, and other exponential processes. It is a powerful tool that can be used to analyze and understand complex systems.

References

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Introduction

In this article, we will evaluate the function $f(x) = 2^x$ for each input listed in the table and graph the resulting ordered pairs on the coordinate plane. We will also answer some frequently asked questions about the function and its graph.

Q&A

Q: What is the function $f(x) = 2^x$ ?

A: The function $f(x) = 2^x$ is an exponential function that represents the power of 2 raised to the power of $x$ .

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

A: The graph of the function $f(x) = 2^x$ is an exponential curve that passes through the points $(0, 1)$ , $(1, 2)$ , $(2, 4)$ , $(3, 8)$ , and $(4, 16)$ . The curve is concave upward and has a steep slope as $x$ increases.

Q: How do I evaluate the function $f(x) = 2^x$ for each input listed in the table?

A: To evaluate the function $f(x) = 2^x$ for each input listed in the table, you can substitute the input value of $x$ into the function and calculate the corresponding output value of $f(x)$ .

Q: What are the ordered pairs that result from evaluating the function $f(x) = 2^x$ for each input listed in the table?

A: The ordered pairs that result from evaluating the function $f(x) = 2^x$ for each input listed in the table are:

$(0, 1)$
$(1, 2)$
$(2, 4)$
$(3, 8)$
$(4, 16)$

Q: How do I graph the resulting ordered pairs on the coordinate plane?

A: To graph the resulting ordered pairs on the coordinate plane, you can plot the points $(0, 1)$ , $(1, 2)$ , $(2, 4)$ , $(3, 8)$ , and $(4, 16)$ and connect them with a smooth curve to form the graph of the function $f(x) = 2^x$ .

Q: What are some real-world applications of the function $f(x) = 2^x$ ?

A: The function $f(x) = 2^x$ has many real-world applications, including:

Modeling population growth and decay
Modeling chemical reactions and other exponential processes
Analyzing and understanding complex systems

Q: How do I use the function $f(x) = 2^x$ to model population growth and decay?

A: To use the function $f(x) = 2^x$ to model population growth and decay, you can substitute the input value of $x$ into the function and calculate the corresponding output value of $f(x)$ . This will give you the population size at a given time.

Q: How do I use the function $f(x) = 2^x$ to model chemical reactions and other exponential processes?

A: To use the function $f(x) = 2^x$ to model chemical reactions and other exponential processes, you can substitute the input value of $x$ into the function and calculate the corresponding output value of $f(x)$ . This will give you the amount of the substance at a given time.

Conclusion

In this article, we evaluated the function $f(x) = 2^x$ for each input listed in the table and graphed the resulting ordered pairs on the coordinate plane. We also answered some frequently asked questions about the function and its graph. The function $f(x) = 2^x$ has many real-world applications, including modeling population growth and decay, modeling chemical reactions and other exponential processes, and analyzing and understanding complex systems.

Introduction

Evaluating the Function for Each Input Listed in the Table

Evaluating f(0)f(0)f(0)

Evaluating f(1)f(1)f(1)

Evaluating f(2)f(2)f(2)

Evaluating f(3)f(3)f(3)

Evaluating f(4)f(4)f(4)

Graphing the Resulting Ordered Pairs on the Coordinate Plane

Plotting the Ordered Pairs

Graphing the Function

Conclusion

Discussion

References

Introduction

Q&A

Q: What is the function f(x)=2xf(x) = 2^xf(x)=2x?

Q: What is the graph of the function f(x)=2xf(x) = 2^xf(x)=2x?

Q: How do I evaluate the function f(x)=2xf(x) = 2^xf(x)=2x for each input listed in the table?

Q: What are the ordered pairs that result from evaluating the function f(x)=2xf(x) = 2^xf(x)=2x for each input listed in the table?

Q: How do I graph the resulting ordered pairs on the coordinate plane?

Q: What are some real-world applications of the function f(x)=2xf(x) = 2^xf(x)=2x?

Q: How do I use the function f(x)=2xf(x) = 2^xf(x)=2x to model population growth and decay?

Q: How do I use the function f(x)=2xf(x) = 2^xf(x)=2x to model chemical reactions and other exponential processes?

Conclusion

Discussion

References

Evaluating $f(0)$

Evaluating $f(1)$

Evaluating $f(2)$

Evaluating $f(3)$

Evaluating $f(4)$

Q: What is the function $f(x) = 2^x$ ?

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

Q: How do I evaluate the function $f(x) = 2^x$ for each input listed in the table?

Q: What are the ordered pairs that result from evaluating the function $f(x) = 2^x$ for each input listed in the table?

Q: What are some real-world applications of the function $f(x) = 2^x$ ?

Q: How do I use the function $f(x) = 2^x$ to model population growth and decay?

Q: How do I use the function $f(x) = 2^x$ to model chemical reactions and other exponential processes?