The Table Below Shows The Points On A Function.$\[ \begin{tabular}{|c|c|} \hline $x$ & $f(x)$ \\ \hline 0 & 1 \\ \hline 2 & -3 \\ \hline -2 & 13 \\ \hline 4 & 1 \\ \hline -1 & 6 \\ \hline 3 & -2 \\ \hline \end{tabular} \\]Identify Points On

Introduction

In mathematics, a function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range. The table below shows the points on a function, which is a crucial concept in understanding various mathematical operations and relationships. In this article, we will delve into the analysis of the given table and identify the points on the function.

The Table of Points

$x$	$f(x)$
0	1
2	-3
-2	13
4	1
-1	6
3	-2

Understanding the Table

The table represents a function, where each input $x$ is associated with a unique output $f(x)$. The table shows the following points:

• When $x = 0$, $f(x) = 1$
• When $x = 2$, $f(x) = -3$
• When $x = -2$, $f(x) = 13$
• When $x = 4$, $f(x) = 1$
• When $x = -1$, $f(x) = 6$
• When $x = 3$, $f(x) = -2$

Analyzing the Points

To analyze the points on the function, we need to examine the relationship between the input $x$ and the output $f(x)$. By looking at the table, we can observe the following:

• The function has a positive output when the input is negative, and a negative output when the input is positive.
• The function has a maximum output of 13 when the input is -2, and a minimum output of -3 when the input is 2.
• The function has a symmetry about the origin, as the output is the same for the input -2 and 2.

Identifying the Points

Based on the analysis of the table, we can identify the points on the function as follows:

• The point $(0, 1)$ is on the function, as $f(0) = 1$.
• The point $(2, -3)$ is on the function, as $f(2) = -3$.
• The point $(-2, 13)$ is on the function, as $f(-2) = 13$.
• The point $(4, 1)$ is on the function, as $f(4) = 1$.
• The point $(-1, 6)$ is on the function, as $f(-1) = 6$.
• The point $(3, -2)$ is on the function, as $f(3) = -2$.

Conclusion

In conclusion, the table of points represents a function, where each input $x$ is associated with a unique output $f(x)$. By analyzing the table, we can identify the points on the function and understand the relationship between the input and output. The function has a positive output when the input is negative, and a negative output when the input is positive. The function has a maximum output of 13 when the input is -2, and a minimum output of -3 when the input is 2. The function has a symmetry about the origin, as the output is the same for the input -2 and 2.

References

• [1] Khan Academy. (n.d.). Functions. Retrieved from https://www.khanacademy.org/math/algebra-functions/functions
• [2] Math Open Reference. (n.d.). Functions. Retrieved from https://www.mathopenref.com/functions.html

Further Reading

• [1] Algebra and Trigonometry by Michael Sullivan. (2014). Pearson Education.
• [2] Calculus by Michael Spivak. (2008). Publish or Perish, Inc.

Glossary

• Function: A relation between a set of inputs, called the domain, and a set of possible outputs, called the range.
• Domain: The set of all possible inputs for a function.
• Range: The set of all possible outputs for a function.
• Symmetry: A property of a function where the output is the same for the input -x and x.
  The Table of Points: A Mathematical Analysis - Q&A =====================================================

Introduction

In our previous article, we analyzed the table of points and identified the points on the function. In this article, we will answer some frequently asked questions related to the table of points and the function.

Q&A

Q: What is the domain of the function?

A: The domain of the function is the set of all possible inputs, which in this case is the set of all real numbers.

Q: What is the range of the function?

A: The range of the function is the set of all possible outputs, which in this case is the set of all real numbers.

Q: Is the function continuous?

A: Based on the table of points, we cannot determine if the function is continuous or not. However, we can observe that the function has a positive output when the input is negative, and a negative output when the input is positive.

Q: Is the function symmetric about the origin?

A: Yes, the function is symmetric about the origin, as the output is the same for the input -2 and 2.

Q: What is the maximum output of the function?

A: The maximum output of the function is 13, which occurs when the input is -2.

Q: What is the minimum output of the function?

A: The minimum output of the function is -3, which occurs when the input is 2.

Q: Can we determine the equation of the function?

A: Based on the table of points, we cannot determine the equation of the function. However, we can use the points to create a graph of the function.

Q: How can we use the table of points to create a graph of the function?

A: We can use the points to create a graph of the function by plotting the points on a coordinate plane and drawing a smooth curve through the points.

Q: What is the significance of the table of points in mathematics?

A: The table of points is a fundamental concept in mathematics, as it represents a function and allows us to analyze the relationship between the input and output.

Q: How can we use the table of points in real-world applications?

A: The table of points can be used in various real-world applications, such as modeling population growth, predicting stock prices, and analyzing data.

Conclusion

In conclusion, the table of points represents a function, where each input $x$ is associated with a unique output $f(x)$. By analyzing the table, we can identify the points on the function and understand the relationship between the input and output. The function has a positive output when the input is negative, and a negative output when the input is positive. The function has a maximum output of 13 when the input is -2, and a minimum output of -3 when the input is 2. The function has a symmetry about the origin, as the output is the same for the input -2 and 2.

References

• [1] Khan Academy. (n.d.). Functions. Retrieved from https://www.khanacademy.org/math/algebra-functions/functions
• [2] Math Open Reference. (n.d.). Functions. Retrieved from https://www.mathopenref.com/functions.html

Further Reading

• [1] Algebra and Trigonometry by Michael Sullivan. (2014). Pearson Education.
• [2] Calculus by Michael Spivak. (2008). Publish or Perish, Inc.

Glossary

• Function: A relation between a set of inputs, called the domain, and a set of possible outputs, called the range.
• Domain: The set of all possible inputs for a function.
• Range: The set of all possible outputs for a function.
• Symmetry: A property of a function where the output is the same for the input -x and x.