Complete The Table Of Values For $f(x)=x^2+5$ And $g(x)=4^x$.$\[ \begin{tabular}{|c|c|c|} \hline $x$ & $f(x)$ & $g(x)$ \\ \hline 0 & $\square$ & $\square$ \\ \hline 1 & $\square$ & $\square$ \\ \hline 2 & $\square$ & $\square$

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Introduction

In this article, we will be completing the table of values for two given functions, $f(x)=x^2+5$ and $g(x)=4^x$. The table of values is a crucial tool in mathematics that helps us understand the behavior of functions and their corresponding outputs for different input values. By completing the table of values, we can gain a deeper understanding of the functions and their properties.

Function $f(x)=x^2+5$

The function $f(x)=x^2+5$ is a quadratic function that takes an input value $x$ and returns the square of $x$ plus $5$. To complete the table of values for this function, we need to find the output values for $x=0$, $x=1$, and $x=2$.

Calculating $f(0)$

To calculate $f(0)$, we substitute $x=0$ into the function $f(x)=x^2+5$. This gives us:

$f(0) = (0)^2 + 5 = 0 + 5 = 5$

So, the value of $f(0)$ is $5$.

Calculating $f(1)$

To calculate $f(1)$, we substitute $x=1$ into the function $f(x)=x^2+5$. This gives us:

$f(1) = (1)^2 + 5 = 1 + 5 = 6$

So, the value of $f(1)$ is $6$.

Calculating $f(2)$

To calculate $f(2)$, we substitute $x=2$ into the function $f(x)=x^2+5$. This gives us:

$f(2) = (2)^2 + 5 = 4 + 5 = 9$

So, the value of $f(2)$ is $9$.

Function $g(x)=4^x$

The function $g(x)=4^x$ is an exponential function that takes an input value $x$ and returns $4$ raised to the power of $x$. To complete the table of values for this function, we need to find the output values for $x=0$, $x=1$, and $x=2$.

Calculating $g(0)$

To calculate $g(0)$, we substitute $x=0$ into the function $g(x)=4^x$. This gives us:

$g(0) = 4^0 = 1$

So, the value of $g(0)$ is $1$.

Calculating $g(1)$

To calculate $g(1)$, we substitute $x=1$ into the function $g(x)=4^x$. This gives us:

$g(1) = 4^1 = 4$

So, the value of $g(1)$ is $4$.

Calculating $g(2)$

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

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

So, the value of $g(2)$ is $16$.

Completing the Table of Values

Now that we have calculated the output values for $f(x)$ and $g(x)$, we can complete the table of values as follows:

$x$	$f(x)$	$g(x)$
0	5	1
1	6	4
2	9	16

Conclusion

In this article, we completed the table of values for the functions $f(x)=x^2+5$ and $g(x)=4^x$. We calculated the output values for $x=0$, $x=1$, and $x=2$ and filled in the table accordingly. This exercise helps us understand the behavior of the functions and their corresponding outputs for different input values. By completing the table of values, we can gain a deeper understanding of the functions and their properties.

Discussion

The table of values is a crucial tool in mathematics that helps us understand the behavior of functions and their corresponding outputs for different input values. By completing the table of values, we can gain a deeper understanding of the functions and their properties.

In this article, we completed the table of values for the functions $f(x)=x^2+5$ and $g(x)=4^x$. We calculated the output values for $x=0$, $x=1$, and $x=2$ and filled in the table accordingly.

The table of values can be used to:

• Understand the behavior of functions and their corresponding outputs for different input values
• Identify patterns and relationships between the input and output values
• Make predictions about the behavior of the functions for different input values

By completing the table of values, we can gain a deeper understanding of the functions and their properties, which can be useful in a variety of mathematical and real-world applications.

References

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

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Q: What is the table of values?

A: The table of values is a table that shows the input values of a function and the corresponding output values. It is a useful tool for understanding the behavior of a function and its corresponding outputs for different input values.

Q: Why is it important to complete the table of values?

A: Completing the table of values is important because it helps us understand the behavior of a function and its corresponding outputs for different input values. It also helps us identify patterns and relationships between the input and output values, which can be useful in a variety of mathematical and real-world applications.

Q: How do I complete the table of values for a function?

A: To complete the table of values for a function, you need to substitute different input values into the function and calculate the corresponding output values. You can use a calculator or a computer program to help you with the calculations.

Q: What are some common mistakes to avoid when completing the table of values?

A: Some common mistakes to avoid when completing the table of values include:

• Not substituting the correct input values into the function
• Not calculating the corresponding output values correctly
• Not filling in the table correctly
• Not checking the table for errors

Q: How can I use the table of values to understand the behavior of a function?

A: You can use the table of values to understand the behavior of a function by looking at the output values for different input values. You can also use the table to identify patterns and relationships between the input and output values.

Q: Can I use the table of values to make predictions about the behavior of a function?

A: Yes, you can use the table of values to make predictions about the behavior of a function. By looking at the output values for different input values, you can make educated guesses about what the output values will be for other input values.

Q: How can I use the table of values in real-world applications?

A: You can use the table of values in a variety of real-world applications, such as:

• Modeling population growth
• Predicting stock prices
• Understanding the behavior of physical systems
• Making decisions based on data

Q: What are some common functions that I can use the table of values with?

A: Some common functions that you can use the table of values with include:

• Linear functions
• Quadratic functions
• Exponential functions
• Trigonometric functions

Q: How can I create a table of values for a function using a calculator or computer program?

A: You can create a table of values for a function using a calculator or computer program by entering the function and the input values, and then using the calculator or program to calculate the corresponding output values.

Q: What are some tips for creating a table of values?

A: Some tips for creating a table of values include:

• Use a clear and consistent format for the table
• Make sure to include all the necessary information in the table
• Check the table for errors
• Use a calculator or computer program to help with the calculations

Q: How can I use the table of values to check my work?

A: You can use the table of values to check your work by comparing the output values in the table to the output values that you calculated. If the output values match, then you know that your work is correct.

Q: What are some common mistakes to avoid when using the table of values?

A: Some common mistakes to avoid when using the table of values include:

• Not using the correct input values
• Not calculating the corresponding output values correctly
• Not filling in the table correctly
• Not checking the table for errors

Q: How can I use the table of values to make decisions?

A: You can use the table of values to make decisions by looking at the output values for different input values and making educated guesses about what the output values will be for other input values.

Q: What are some real-world applications of the table of values?

A: Some real-world applications of the table of values include:

• Modeling population growth
• Predicting stock prices
• Understanding the behavior of physical systems
• Making decisions based on data

Q: How can I use the table of values to understand the behavior of a function?

A: You can use the table of values to understand the behavior of a function by looking at the output values for different input values and identifying patterns and relationships between the input and output values.

Q: What are some common functions that I can use the table of values with?

A: Some common functions that you can use the table of values with include:

• Linear functions
• Quadratic functions
• Exponential functions
• Trigonometric functions

Q: How can I create a table of values for a function using a calculator or computer program?

A: You can create a table of values for a function using a calculator or computer program by entering the function and the input values, and then using the calculator or program to calculate the corresponding output values.

Q: What are some tips for creating a table of values?

A: Some tips for creating a table of values include:

• Use a clear and consistent format for the table
• Make sure to include all the necessary information in the table
• Check the table for errors
• Use a calculator or computer program to help with the calculations

Q: How can I use the table of values to check my work?

A: You can use the table of values to check your work by comparing the output values in the table to the output values that you calculated. If the output values match, then you know that your work is correct.

Q: What are some common mistakes to avoid when using the table of values?

A: Some common mistakes to avoid when using the table of values include:

• Not using the correct input values
• Not calculating the corresponding output values correctly
• Not filling in the table correctly
• Not checking the table for errors

Q: How can I use the table of values to make decisions?

A: You can use the table of values to make decisions by looking at the output values for different input values and making educated guesses about what the output values will be for other input values.

Q: What are some real-world applications of the table of values?

A: Some real-world applications of the table of values include:

• Modeling population growth
• Predicting stock prices
• Understanding the behavior of physical systems
• Making decisions based on data

Q: How can I use the table of values to understand the behavior of a function?

A: You can use the table of values to understand the behavior of a function by looking at the output values for different input values and identifying patterns and relationships between the input and output values.

Q: What are some common functions that I can use the table of values with?

A: Some common functions that you can use the table of values with include:

• Linear functions
• Quadratic functions
• Exponential functions
• Trigonometric functions

Q: How can I create a table of values for a function using a calculator or computer program?

A: You can create a table of values for a function using a calculator or computer program by entering the function and the input values, and then using the calculator or program to calculate the corresponding output values.

Q: What are some tips for creating a table of values?

A: Some tips for creating a table of values include:

• Use a clear and consistent format for the table
• Make sure to include all the necessary information in the table
• Check the table for errors
• Use a calculator or computer program to help with the calculations

Q: How can I use the table of values to check my work?

A: You can use the table of values to check your work by comparing the output values in the table to the output values that you calculated. If the output values match, then you know that your work is correct.

Q: What are some common mistakes to avoid when using the table of values?

A: Some common mistakes to avoid when using the table of values include:

• Not using the correct input values
• Not calculating the corresponding output values correctly
• Not filling in the table correctly
• Not checking the table for errors

Q: How can I use the table of values to make decisions?

A: You can use the table of values to make decisions by looking at the output values for different input values and making educated guesses about what the output values will be for other input values.

Q: What are some real-world applications of the table of values?

A: Some real-world applications of the table of values include:

• Modeling population growth
• Predicting stock prices
• Understanding the behavior of physical systems
• Making decisions based on data

Q: How can I use the table of values to understand the behavior of a function?

A: You can use the table of values to understand the behavior of a function by looking at the output values for different input values and identifying patterns and relationships between the input and output values.

Q: What are some common functions that I can use the table of values with?

A: Some common functions that you can use the table of values with include:

• Linear functions
• Quadratic functions
• Exponential functions
• Trigonometric functions